The future value of $400 each 6months for 5 years semiannually compounded at the nominal rate of 12%.

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Answer 1

Question

Chapter 4, Problem 18P

a)

Summary Introduction

To determine: The future value of $400 each 6months for 5 years semiannually compounded at the nominal rate of 12%.

b)

Summary Introduction

To determine: The future value of $200 for each 3 months for 5 years quarterly compounded at a nominal rate of 12%.

c)

Summary Introduction

To determine: The reason why the annuity in part b acquires 101.75 extra than part a during the 5 years.

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Find the future values of the following ordinary annuities:a. FV of $400 paid each 6 months for 5 years at a nominal rate of 12% compounded semiannuallyb. FV of $200 paid each 3 months for 5 years at a nominal rate of 12% compounded quarterlyc. These annuities receive the same amount of cash during the 5-year period and earn interest at the same nominal rate, yet the annuity in part b ends up larger than the one in part a. Why does this occur?

The present values of the following three annuities are equal: • perpetuity immediate paying 1 year year, calculated at an annual effective interest rate of 7.25%. • 50-year annuity immediate paying 1 each year, calculated at an annual effective interest rate of j%. • n−year annuity immediate paying 1 each year, calculated at an annual effective interest rate of j − 1%. Calculate n.

Calculate the future value of the following annuities, assuming each annuity payment is made at the end of each compounding period. Annuity Payment Annual Rate Interest Compounded Period Invested 1. $3,000 7% Annually 6 years 2. 6,000 8 Semiannually 9 years 3. 5,000 12 Quarterly 5 years

Answer 2

Question

Chapter 4, Problem 18P

a)

Summary Introduction

To determine: The future value of $400 each 6months for 5 years semiannually compounded at the nominal rate of 12%.

b)

Summary Introduction

To determine: The future value of $200 for each 3 months for 5 years quarterly compounded at a nominal rate of 12%.

c)

Summary Introduction

To determine: The reason why the annuity in part b acquires 101.75 extra than part a during the 5 years.

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Answer 3

Question

Chapter 4, Problem 18P

a)

Summary Introduction

To determine: The future value of $400 each 6months for 5 years semiannually compounded at the nominal rate of 12%.

b)

Summary Introduction

To determine: The future value of $200 for each 3 months for 5 years quarterly compounded at a nominal rate of 12%.

c)

Summary Introduction

To determine: The reason why the annuity in part b acquires 101.75 extra than part a during the 5 years.

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Answer 4

Question

Chapter 4, Problem 18P

a)

Summary Introduction

To determine: The future value of $400 each 6months for 5 years semiannually compounded at the nominal rate of 12%.

b)

Summary Introduction

To determine: The future value of $200 for each 3 months for 5 years quarterly compounded at a nominal rate of 12%.

c)

Summary Introduction

To determine: The reason why the annuity in part b acquires 101.75 extra than part a during the 5 years.

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Answer 5

Chapter 4, Problem 18P

a)

Summary Introduction

To determine: The future value of $400 each 6months for 5 years semiannually compounded at the nominal rate of 12%.

b)

Summary Introduction

To determine: The future value of $200 for each 3 months for 5 years quarterly compounded at a nominal rate of 12%.

c)

Summary Introduction

To determine: The reason why the annuity in part b acquires 101.75 extra than part a during the 5 years.

Answer 6

Chapter 4, Problem 18P

a)

Summary Introduction

To determine: The future value of $400 each 6months for 5 years semiannually compounded at the nominal rate of 12%.

Answer 7

Chapter 4, Problem 18P

a)

Summary Introduction

To determine: The future value of $400 each 6months for 5 years semiannually compounded at the nominal rate of 12%.

Answer 8

b)

Summary Introduction

To determine: The future value of $200 for each 3 months for 5 years quarterly compounded at a nominal rate of 12%.

Answer 9

b)

Summary Introduction

To determine: The future value of $200 for each 3 months for 5 years quarterly compounded at a nominal rate of 12%.

Answer 10

c)

Summary Introduction

To determine: The reason why the annuity in part b acquires 101.75 extra than part a during the 5 years.

Answer 11

c)

Summary Introduction

To determine: The reason why the annuity in part b acquires 101.75 extra than part a during the 5 years.

Answer 12

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Answer 13

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Answer 14

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Answer 15

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The future value of $400 each 6months for 5 years semiannually compounded at the nominal rate of 12%.

Solution Summary: The author calculates the future value of 400 for 5 years semiannually compounded at a nominal rate of 12%. The present value is 5,374.07.

To determine: The future value of $400 each 6months for 5 years semiannually compounded at the nominal rate of 12%.

To determine: The future value of $200 for each 3 months for 5 years quarterly compounded at a nominal rate of 12%.

To determine: The reason why the annuity in part b acquires 101.75 extra than part a during the 5 years.

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