The rate of return of a bond Introduction: Rate of return refers to the gain or loss on the investment. It also refers to the increase or decrease in the capital value of an investment. The future value of money refers to the amount of dollars that an investment grows over a definite period at a particular rate of interest rate. In other words, it refers to the future value of present cash investments.

Question

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Answer 1

Question

Chapter 5, Problem 16QP

a)

Summary Introduction

To calculate: The rate of return of a bond

Introduction:

Rate of return refers to the gain or loss on the investment. It also refers to the increase or decrease in the capital value of an investment.

The future value of money refers to the amount of dollars that an investment grows over a definite period at a particular rate of interest rate. In other words, it refers to the future value of present cash investments.

a)

Expert Solution

Answer to Problem 16QP

A bond with a face value of $50 would double its value in 20 years if the rate of return is 3.53%.

Explanation of Solution

Given information:

Person X purchased a bond worth $50. He plans to hold it for 20 years until the value of the bond doubles.

The formula to calculate the rate of return:

P×(1+r)t=FV

Where,

“P” refers to the principal amount invested

“r” refers to the simple rate of interest

“t” refers to the number of years or periods of investment

“FV” refers to the future value or the current market value

Compute the rate of return:

The present value of the bond is $50. He plans to invest for 20 years until the value of the bond doubles. Hence, the future value of the bond will be $100 ($50×2) .

P×(1+r)t=FV$50×(1+r)20=$100(1+r)20=$100$50(1+r)20=2

1+r=2120r=1.0353−1r=0.0353 or 3.53%

Hence, the rate of return is 3.53% per year.

b)

Summary Introduction

To calculate: The future value of the bond

Introduction:

Rate of return refers to the gain or loss on the investment. It also refers to the increase or decrease in the capital value of an investment.

The future value of money refers to the amount of dollars that an investment grows over a definite period at a particular rate of interest rate. In other words, it refers to the future value of present cash investments.

b)

Expert Solution

Answer to Problem 16QP

The value of the bond in 2024 will be $50.5.

Explanation of Solution

Given information:

Person X will purchase a bond worth $50 in 2014. He plans to hold it until 2024 or for 10 years. The rate of interest on the bond is 0.10 percent per year.

The formula to calculate the future value:

FV=PV×(1+r)t

Where,

“FV” refers to the future value or the current market value

“PV” refers to the present value

“r” refers to the simple rate of interest

“t” refers to the number of years or periods of investment

Compute the future value:

FV=PV×(1+r)t=$50×(1+0.001)10=$50×1.0100=$50.5

Hence, the future value of investment after 10 years is $50.5.

c)

Summary Introduction

To calculate: The rate of return

Introduction:

Rate of return refers to the gain or loss on the investment. It also refers to the increase or decrease in the capital value of an investment.

The future value of money refers to the amount of dollars that an investment grows over a definite period at a particular rate of interest rate. In other words, it refers to the future value of present cash investments.

c)

Expert Solution

Answer to Problem 16QP

The bond has to fetch a return of 7.18% per year to double its value in 2034.

Explanation of Solution

Given information:

Person X purchased a bond worth $50 in 2014. He plans to hold it until 2024 or for 10 years. The rate of interest on the bond is 0.10 percent per year. The future value of this bond in 2024 will be $50.50 (Refer to Part (b) of the solution). Instead of cashing the bond at $50.50, he plans to reinvest the bond value until the value of the bond doubles in 2034.

The formula to calculate the rate of return:

P×(1+r)t=FV

Where,

“P” refers to the principal amount invested

“r” refers to the simple rate of interest

“t” refers to the number of years or periods of investment

“FV” refers to the future value or the current market value

Compute the rate of return:

The present value of the bond is $50.50 in 2024. He plans to invest for 10 years until the value of the bond doubles in 2034. Hence, the future value of the bond will be $101 ($50.50×2) .

P×(1+r)t=FV$50.50×(1+r)10=$101(1+r)10=$101$50.50(1+r)10=2

1+r=2110r=1.0718−1r=0.0718 or 7.18%

Hence, the bond has to fetch a return of 7.18% per year to double its value in 2034.

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Students have asked these similar questions

Suppose the government decides to issue a new savings bond that is guaranteed to double in value if you hold it for 16 years. Assume you purchase a bond that costs $75. a. What is the exact rate of return you would earn if you held the bond for 16 years until b. If you purchased the bond for $75 in 2017 at the then current interest rate of.21 c. In 2025, instead of cashing in the bond for its then current value, you decide to hold it doubled in value? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) percent year, how much would the bond be worth in 2025? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) the bond until it doubles in face value in 2033. What annual rate of return will you earn over the last 8 years? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places,e.g..32.16.) a. Rate of return b. Value of bond c. Rate…

3. Present Value of Annuity and Perpetuity - Show your steps! (You must simplify your answer use the formula for Geometric series.) 1 A bond with a face value of y pays out interest at rate r annually. The discount rate you should use for the bond is i. (That is, the present value of $1 received a year from now is $11, and the present value of 1 dollar received 2 years from now is $- .) What is the present value of owning the bond that pays its first interest a year from now if (a) The bond pays interest for n years and pays back the face value at the last year. (b) The bond pays interest forever and never pays back the face value. (1+i)²

You are deciding whether to buy a bond. The bond will pay out $1,000 in 5 years. But there is uncertainty over the interest rate. Between now and year 1 (period 0 and period 1), uncertainty will be resolved immediately after time 0. There is • 50 percent chance r = 0.1 • 50 percent chance r = 0.05 Interest compounds annually. What is the expected value of the bond?.

Answer 2

Question

Chapter 5, Problem 16QP

a)

Summary Introduction

To calculate: The rate of return of a bond

Introduction:

Rate of return refers to the gain or loss on the investment. It also refers to the increase or decrease in the capital value of an investment.

The future value of money refers to the amount of dollars that an investment grows over a definite period at a particular rate of interest rate. In other words, it refers to the future value of present cash investments.

a)

Expert Solution

Answer to Problem 16QP

A bond with a face value of $50 would double its value in 20 years if the rate of return is 3.53%.

Explanation of Solution

Given information:

Person X purchased a bond worth $50. He plans to hold it for 20 years until the value of the bond doubles.

The formula to calculate the rate of return:

P×(1+r)t=FV

Where,

“P” refers to the principal amount invested

“r” refers to the simple rate of interest

“t” refers to the number of years or periods of investment

“FV” refers to the future value or the current market value

Compute the rate of return:

The present value of the bond is $50. He plans to invest for 20 years until the value of the bond doubles. Hence, the future value of the bond will be $100 ($50×2) .

P×(1+r)t=FV$50×(1+r)20=$100(1+r)20=$100$50(1+r)20=2

1+r=2120r=1.0353−1r=0.0353 or 3.53%

Hence, the rate of return is 3.53% per year.

b)

Summary Introduction

To calculate: The future value of the bond

Introduction:

Rate of return refers to the gain or loss on the investment. It also refers to the increase or decrease in the capital value of an investment.

The future value of money refers to the amount of dollars that an investment grows over a definite period at a particular rate of interest rate. In other words, it refers to the future value of present cash investments.

b)

Expert Solution

Answer to Problem 16QP

The value of the bond in 2024 will be $50.5.

Explanation of Solution

Given information:

Person X will purchase a bond worth $50 in 2014. He plans to hold it until 2024 or for 10 years. The rate of interest on the bond is 0.10 percent per year.

The formula to calculate the future value:

FV=PV×(1+r)t

Where,

“FV” refers to the future value or the current market value

“PV” refers to the present value

“r” refers to the simple rate of interest

“t” refers to the number of years or periods of investment

Compute the future value:

FV=PV×(1+r)t=$50×(1+0.001)10=$50×1.0100=$50.5

Hence, the future value of investment after 10 years is $50.5.

c)

Summary Introduction

To calculate: The rate of return

Introduction:

Rate of return refers to the gain or loss on the investment. It also refers to the increase or decrease in the capital value of an investment.

The future value of money refers to the amount of dollars that an investment grows over a definite period at a particular rate of interest rate. In other words, it refers to the future value of present cash investments.

c)

Expert Solution

Answer to Problem 16QP

The bond has to fetch a return of 7.18% per year to double its value in 2034.

Explanation of Solution

Given information:

Person X purchased a bond worth $50 in 2014. He plans to hold it until 2024 or for 10 years. The rate of interest on the bond is 0.10 percent per year. The future value of this bond in 2024 will be $50.50 (Refer to Part (b) of the solution). Instead of cashing the bond at $50.50, he plans to reinvest the bond value until the value of the bond doubles in 2034.

The formula to calculate the rate of return:

P×(1+r)t=FV

Where,

“P” refers to the principal amount invested

“r” refers to the simple rate of interest

“t” refers to the number of years or periods of investment

“FV” refers to the future value or the current market value

Compute the rate of return:

The present value of the bond is $50.50 in 2024. He plans to invest for 10 years until the value of the bond doubles in 2034. Hence, the future value of the bond will be $101 ($50.50×2) .

P×(1+r)t=FV$50.50×(1+r)10=$101(1+r)10=$101$50.50(1+r)10=2

1+r=2110r=1.0718−1r=0.0718 or 7.18%

Hence, the bond has to fetch a return of 7.18% per year to double its value in 2034.

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Answer 3

Question

Chapter 5, Problem 16QP

a)

Summary Introduction

To calculate: The rate of return of a bond

Introduction:

Rate of return refers to the gain or loss on the investment. It also refers to the increase or decrease in the capital value of an investment.

The future value of money refers to the amount of dollars that an investment grows over a definite period at a particular rate of interest rate. In other words, it refers to the future value of present cash investments.

a)

Expert Solution

Answer to Problem 16QP

A bond with a face value of $50 would double its value in 20 years if the rate of return is 3.53%.

Explanation of Solution

Given information:

Person X purchased a bond worth $50. He plans to hold it for 20 years until the value of the bond doubles.

The formula to calculate the rate of return:

P×(1+r)t=FV

Where,

“P” refers to the principal amount invested

“r” refers to the simple rate of interest

“t” refers to the number of years or periods of investment

“FV” refers to the future value or the current market value

Compute the rate of return:

The present value of the bond is $50. He plans to invest for 20 years until the value of the bond doubles. Hence, the future value of the bond will be $100 ($50×2) .

P×(1+r)t=FV$50×(1+r)20=$100(1+r)20=$100$50(1+r)20=2

1+r=2120r=1.0353−1r=0.0353 or 3.53%

Hence, the rate of return is 3.53% per year.

b)

Summary Introduction

To calculate: The future value of the bond

Introduction:

Rate of return refers to the gain or loss on the investment. It also refers to the increase or decrease in the capital value of an investment.

The future value of money refers to the amount of dollars that an investment grows over a definite period at a particular rate of interest rate. In other words, it refers to the future value of present cash investments.

b)

Expert Solution

Answer to Problem 16QP

The value of the bond in 2024 will be $50.5.

Explanation of Solution

Given information:

Person X will purchase a bond worth $50 in 2014. He plans to hold it until 2024 or for 10 years. The rate of interest on the bond is 0.10 percent per year.

The formula to calculate the future value:

FV=PV×(1+r)t

Where,

“FV” refers to the future value or the current market value

“PV” refers to the present value

“r” refers to the simple rate of interest

“t” refers to the number of years or periods of investment

Compute the future value:

FV=PV×(1+r)t=$50×(1+0.001)10=$50×1.0100=$50.5

Hence, the future value of investment after 10 years is $50.5.

c)

Summary Introduction

To calculate: The rate of return

Introduction:

Rate of return refers to the gain or loss on the investment. It also refers to the increase or decrease in the capital value of an investment.

The future value of money refers to the amount of dollars that an investment grows over a definite period at a particular rate of interest rate. In other words, it refers to the future value of present cash investments.

c)

Expert Solution

Answer to Problem 16QP

The bond has to fetch a return of 7.18% per year to double its value in 2034.

Explanation of Solution

Given information:

Person X purchased a bond worth $50 in 2014. He plans to hold it until 2024 or for 10 years. The rate of interest on the bond is 0.10 percent per year. The future value of this bond in 2024 will be $50.50 (Refer to Part (b) of the solution). Instead of cashing the bond at $50.50, he plans to reinvest the bond value until the value of the bond doubles in 2034.

The formula to calculate the rate of return:

P×(1+r)t=FV

Where,

“P” refers to the principal amount invested

“r” refers to the simple rate of interest

“t” refers to the number of years or periods of investment

“FV” refers to the future value or the current market value

Compute the rate of return:

The present value of the bond is $50.50 in 2024. He plans to invest for 10 years until the value of the bond doubles in 2034. Hence, the future value of the bond will be $101 ($50.50×2) .

P×(1+r)t=FV$50.50×(1+r)10=$101(1+r)10=$101$50.50(1+r)10=2

1+r=2110r=1.0718−1r=0.0718 or 7.18%

Hence, the bond has to fetch a return of 7.18% per year to double its value in 2034.

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Answer 4

Question

Chapter 5, Problem 16QP

a)

Summary Introduction

To calculate: The rate of return of a bond

Introduction:

Rate of return refers to the gain or loss on the investment. It also refers to the increase or decrease in the capital value of an investment.

The future value of money refers to the amount of dollars that an investment grows over a definite period at a particular rate of interest rate. In other words, it refers to the future value of present cash investments.

a)

Expert Solution

Answer to Problem 16QP

A bond with a face value of $50 would double its value in 20 years if the rate of return is 3.53%.

Explanation of Solution

Given information:

Person X purchased a bond worth $50. He plans to hold it for 20 years until the value of the bond doubles.

The formula to calculate the rate of return:

P×(1+r)t=FV

Where,

“P” refers to the principal amount invested

“r” refers to the simple rate of interest

“t” refers to the number of years or periods of investment

“FV” refers to the future value or the current market value

Compute the rate of return:

The present value of the bond is $50. He plans to invest for 20 years until the value of the bond doubles. Hence, the future value of the bond will be $100 ($50×2) .

P×(1+r)t=FV$50×(1+r)20=$100(1+r)20=$100$50(1+r)20=2

1+r=2120r=1.0353−1r=0.0353 or 3.53%

Hence, the rate of return is 3.53% per year.

b)

Summary Introduction

To calculate: The future value of the bond

Introduction:

Rate of return refers to the gain or loss on the investment. It also refers to the increase or decrease in the capital value of an investment.

The future value of money refers to the amount of dollars that an investment grows over a definite period at a particular rate of interest rate. In other words, it refers to the future value of present cash investments.

b)

Expert Solution

Answer to Problem 16QP

The value of the bond in 2024 will be $50.5.

Explanation of Solution

Given information:

Person X will purchase a bond worth $50 in 2014. He plans to hold it until 2024 or for 10 years. The rate of interest on the bond is 0.10 percent per year.

The formula to calculate the future value:

FV=PV×(1+r)t

Where,

“FV” refers to the future value or the current market value

“PV” refers to the present value

“r” refers to the simple rate of interest

“t” refers to the number of years or periods of investment

Compute the future value:

FV=PV×(1+r)t=$50×(1+0.001)10=$50×1.0100=$50.5

Hence, the future value of investment after 10 years is $50.5.

c)

Summary Introduction

To calculate: The rate of return

Introduction:

Rate of return refers to the gain or loss on the investment. It also refers to the increase or decrease in the capital value of an investment.

The future value of money refers to the amount of dollars that an investment grows over a definite period at a particular rate of interest rate. In other words, it refers to the future value of present cash investments.

c)

Expert Solution

Answer to Problem 16QP

The bond has to fetch a return of 7.18% per year to double its value in 2034.

Explanation of Solution

Given information:

Person X purchased a bond worth $50 in 2014. He plans to hold it until 2024 or for 10 years. The rate of interest on the bond is 0.10 percent per year. The future value of this bond in 2024 will be $50.50 (Refer to Part (b) of the solution). Instead of cashing the bond at $50.50, he plans to reinvest the bond value until the value of the bond doubles in 2034.

The formula to calculate the rate of return:

P×(1+r)t=FV

Where,

“P” refers to the principal amount invested

“r” refers to the simple rate of interest

“t” refers to the number of years or periods of investment

“FV” refers to the future value or the current market value

Compute the rate of return:

The present value of the bond is $50.50 in 2024. He plans to invest for 10 years until the value of the bond doubles in 2034. Hence, the future value of the bond will be $101 ($50.50×2) .

P×(1+r)t=FV$50.50×(1+r)10=$101(1+r)10=$101$50.50(1+r)10=2

1+r=2110r=1.0718−1r=0.0718 or 7.18%

Hence, the bond has to fetch a return of 7.18% per year to double its value in 2034.

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Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 5

Chapter 5, Problem 16QP

a)

Summary Introduction

To calculate: The rate of return of a bond

Introduction:

Rate of return refers to the gain or loss on the investment. It also refers to the increase or decrease in the capital value of an investment.

The future value of money refers to the amount of dollars that an investment grows over a definite period at a particular rate of interest rate. In other words, it refers to the future value of present cash investments.

a)

Expert Solution

Answer to Problem 16QP

A bond with a face value of $50 would double its value in 20 years if the rate of return is 3.53%.

Explanation of Solution

Given information:

Person X purchased a bond worth $50. He plans to hold it for 20 years until the value of the bond doubles.

The formula to calculate the rate of return:

P×(1+r)t=FV

Where,

“P” refers to the principal amount invested

“r” refers to the simple rate of interest

“t” refers to the number of years or periods of investment

“FV” refers to the future value or the current market value

Compute the rate of return:

The present value of the bond is $50. He plans to invest for 20 years until the value of the bond doubles. Hence, the future value of the bond will be $100 ($50×2) .

P×(1+r)t=FV$50×(1+r)20=$100(1+r)20=$100$50(1+r)20=2

1+r=2120r=1.0353−1r=0.0353 or 3.53%

Hence, the rate of return is 3.53% per year.

b)

Summary Introduction

To calculate: The future value of the bond

Introduction:

Rate of return refers to the gain or loss on the investment. It also refers to the increase or decrease in the capital value of an investment.

The future value of money refers to the amount of dollars that an investment grows over a definite period at a particular rate of interest rate. In other words, it refers to the future value of present cash investments.

b)

Expert Solution

Answer to Problem 16QP

The value of the bond in 2024 will be $50.5.

Explanation of Solution

Given information:

Person X will purchase a bond worth $50 in 2014. He plans to hold it until 2024 or for 10 years. The rate of interest on the bond is 0.10 percent per year.

The formula to calculate the future value:

FV=PV×(1+r)t

Where,

“FV” refers to the future value or the current market value

“PV” refers to the present value

“r” refers to the simple rate of interest

“t” refers to the number of years or periods of investment

Compute the future value:

FV=PV×(1+r)t=$50×(1+0.001)10=$50×1.0100=$50.5

Hence, the future value of investment after 10 years is $50.5.

c)

Summary Introduction

To calculate: The rate of return

Introduction:

Rate of return refers to the gain or loss on the investment. It also refers to the increase or decrease in the capital value of an investment.

The future value of money refers to the amount of dollars that an investment grows over a definite period at a particular rate of interest rate. In other words, it refers to the future value of present cash investments.

c)

Expert Solution

Answer to Problem 16QP

The bond has to fetch a return of 7.18% per year to double its value in 2034.

Explanation of Solution

Given information:

Person X purchased a bond worth $50 in 2014. He plans to hold it until 2024 or for 10 years. The rate of interest on the bond is 0.10 percent per year. The future value of this bond in 2024 will be $50.50 (Refer to Part (b) of the solution). Instead of cashing the bond at $50.50, he plans to reinvest the bond value until the value of the bond doubles in 2034.

The formula to calculate the rate of return:

P×(1+r)t=FV

Where,

“P” refers to the principal amount invested

“r” refers to the simple rate of interest

“t” refers to the number of years or periods of investment

“FV” refers to the future value or the current market value

Compute the rate of return:

The present value of the bond is $50.50 in 2024. He plans to invest for 10 years until the value of the bond doubles in 2034. Hence, the future value of the bond will be $101 ($50.50×2) .

P×(1+r)t=FV$50.50×(1+r)10=$101(1+r)10=$101$50.50(1+r)10=2

1+r=2110r=1.0718−1r=0.0718 or 7.18%

Hence, the bond has to fetch a return of 7.18% per year to double its value in 2034.

Answer 6

Chapter 5, Problem 16QP

a)

Summary Introduction

To calculate: The rate of return of a bond

Introduction:

Rate of return refers to the gain or loss on the investment. It also refers to the increase or decrease in the capital value of an investment.

The future value of money refers to the amount of dollars that an investment grows over a definite period at a particular rate of interest rate. In other words, it refers to the future value of present cash investments.

a)

Expert Solution

Answer to Problem 16QP

A bond with a face value of $50 would double its value in 20 years if the rate of return is 3.53%.

Explanation of Solution

Given information:

Person X purchased a bond worth $50. He plans to hold it for 20 years until the value of the bond doubles.

The formula to calculate the rate of return:

P×(1+r)t=FV

Where,

“P” refers to the principal amount invested

“r” refers to the simple rate of interest

“t” refers to the number of years or periods of investment

“FV” refers to the future value or the current market value

Compute the rate of return:

The present value of the bond is $50. He plans to invest for 20 years until the value of the bond doubles. Hence, the future value of the bond will be $100 ($50×2) .

P×(1+r)t=FV$50×(1+r)20=$100(1+r)20=$100$50(1+r)20=2

1+r=2120r=1.0353−1r=0.0353 or 3.53%

Hence, the rate of return is 3.53% per year.

Answer 7

Chapter 5, Problem 16QP

a)

Summary Introduction

To calculate: The rate of return of a bond

Introduction:

Rate of return refers to the gain or loss on the investment. It also refers to the increase or decrease in the capital value of an investment.

The future value of money refers to the amount of dollars that an investment grows over a definite period at a particular rate of interest rate. In other words, it refers to the future value of present cash investments.

Answer 8

a)

Expert Solution

Answer to Problem 16QP

A bond with a face value of $50 would double its value in 20 years if the rate of return is 3.53%.

Answer 9

a)

Expert Solution

Answer 10

a)

Expert Solution

Answer 11

Expert Solution

Answer 12

Explanation of Solution

Given information:

Person X purchased a bond worth $50. He plans to hold it for 20 years until the value of the bond doubles.

The formula to calculate the rate of return:

P×(1+r)t=FV

Where,

“P” refers to the principal amount invested

“r” refers to the simple rate of interest

“t” refers to the number of years or periods of investment

“FV” refers to the future value or the current market value

Compute the rate of return:

The present value of the bond is $50. He plans to invest for 20 years until the value of the bond doubles. Hence, the future value of the bond will be $100 ($50×2) .

P×(1+r)t=FV$50×(1+r)20=$100(1+r)20=$100$50(1+r)20=2

1+r=2120r=1.0353−1r=0.0353 or 3.53%

Hence, the rate of return is 3.53% per year.

Answer 13

b)

Summary Introduction

To calculate: The future value of the bond

Introduction:

Rate of return refers to the gain or loss on the investment. It also refers to the increase or decrease in the capital value of an investment.

The future value of money refers to the amount of dollars that an investment grows over a definite period at a particular rate of interest rate. In other words, it refers to the future value of present cash investments.

b)

Expert Solution

Answer to Problem 16QP

The value of the bond in 2024 will be $50.5.

Explanation of Solution

Given information:

Person X will purchase a bond worth $50 in 2014. He plans to hold it until 2024 or for 10 years. The rate of interest on the bond is 0.10 percent per year.

The formula to calculate the future value:

FV=PV×(1+r)t

Where,

“FV” refers to the future value or the current market value

“PV” refers to the present value

“r” refers to the simple rate of interest

“t” refers to the number of years or periods of investment

Compute the future value:

FV=PV×(1+r)t=$50×(1+0.001)10=$50×1.0100=$50.5

Hence, the future value of investment after 10 years is $50.5.

Answer 14

b)

Summary Introduction

To calculate: The future value of the bond

Introduction:

Rate of return refers to the gain or loss on the investment. It also refers to the increase or decrease in the capital value of an investment.

The future value of money refers to the amount of dollars that an investment grows over a definite period at a particular rate of interest rate. In other words, it refers to the future value of present cash investments.

Answer 15

b)

Expert Solution

Answer to Problem 16QP

The value of the bond in 2024 will be $50.5.

Answer 16

b)

Expert Solution

Answer 17

b)

Expert Solution

Answer 18

Expert Solution

Answer 19

Explanation of Solution

Given information:

Person X will purchase a bond worth $50 in 2014. He plans to hold it until 2024 or for 10 years. The rate of interest on the bond is 0.10 percent per year.

The formula to calculate the future value:

FV=PV×(1+r)t

Where,

“FV” refers to the future value or the current market value

“PV” refers to the present value

“r” refers to the simple rate of interest

“t” refers to the number of years or periods of investment

Compute the future value:

FV=PV×(1+r)t=$50×(1+0.001)10=$50×1.0100=$50.5

Hence, the future value of investment after 10 years is $50.5.

Answer 20

c)

Summary Introduction

To calculate: The rate of return

Introduction:

Rate of return refers to the gain or loss on the investment. It also refers to the increase or decrease in the capital value of an investment.

The future value of money refers to the amount of dollars that an investment grows over a definite period at a particular rate of interest rate. In other words, it refers to the future value of present cash investments.

c)

Expert Solution

Answer to Problem 16QP

The bond has to fetch a return of 7.18% per year to double its value in 2034.

Explanation of Solution

Given information:

Person X purchased a bond worth $50 in 2014. He plans to hold it until 2024 or for 10 years. The rate of interest on the bond is 0.10 percent per year. The future value of this bond in 2024 will be $50.50 (Refer to Part (b) of the solution). Instead of cashing the bond at $50.50, he plans to reinvest the bond value until the value of the bond doubles in 2034.

The formula to calculate the rate of return:

P×(1+r)t=FV

Where,

“P” refers to the principal amount invested

“r” refers to the simple rate of interest

“t” refers to the number of years or periods of investment

“FV” refers to the future value or the current market value

Compute the rate of return:

The present value of the bond is $50.50 in 2024. He plans to invest for 10 years until the value of the bond doubles in 2034. Hence, the future value of the bond will be $101 ($50.50×2) .

P×(1+r)t=FV$50.50×(1+r)10=$101(1+r)10=$101$50.50(1+r)10=2

1+r=2110r=1.0718−1r=0.0718 or 7.18%

Hence, the bond has to fetch a return of 7.18% per year to double its value in 2034.

Answer 21

c)

Summary Introduction

To calculate: The rate of return

Introduction:

Rate of return refers to the gain or loss on the investment. It also refers to the increase or decrease in the capital value of an investment.

The future value of money refers to the amount of dollars that an investment grows over a definite period at a particular rate of interest rate. In other words, it refers to the future value of present cash investments.

Answer 22

c)

Expert Solution

Answer to Problem 16QP

The bond has to fetch a return of 7.18% per year to double its value in 2034.

Answer 23

c)

Expert Solution

Answer 24

c)

Expert Solution

Answer 25

Expert Solution

Answer 26

Explanation of Solution

Given information:

Person X purchased a bond worth $50 in 2014. He plans to hold it until 2024 or for 10 years. The rate of interest on the bond is 0.10 percent per year. The future value of this bond in 2024 will be $50.50 (Refer to Part (b) of the solution). Instead of cashing the bond at $50.50, he plans to reinvest the bond value until the value of the bond doubles in 2034.

The formula to calculate the rate of return:

P×(1+r)t=FV

Where,

“P” refers to the principal amount invested

“r” refers to the simple rate of interest

“t” refers to the number of years or periods of investment

“FV” refers to the future value or the current market value

Compute the rate of return:

The present value of the bond is $50.50 in 2024. He plans to invest for 10 years until the value of the bond doubles in 2034. Hence, the future value of the bond will be $101 ($50.50×2) .

P×(1+r)t=FV$50.50×(1+r)10=$101(1+r)10=$101$50.50(1+r)10=2