# FUTURE VALUE OF AN ANNUITY Kind 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 semiannually b. FV of$200 paid each 3 months for 5 years at a nominal rate of 12% compounded quarterly c. 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?

### Fundamentals of Financial Manageme...

15th Edition
Eugene F. Brigham + 1 other
Publisher: Cengage Learning
ISBN: 9781337395250

### Fundamentals of Financial Manageme...

15th Edition
Eugene F. Brigham + 1 other
Publisher: Cengage Learning
ISBN: 9781337395250

#### Solutions

Chapter
Section
Chapter 5, Problem 25P
Textbook Problem

## FUTURE VALUE OF AN ANNUITY Kind 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 semiannually b. FV of$200 paid each 3 months for 5 years at a nominal rate of 12% compounded quarterly c. 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?

Expert Solution

a.

Summary Introduction

To compute: Future value of annuity of $400 paid each 6 months for 5 years at a nominal rate of 12% compounded semiannually. Future value of annuity: It states the value of regular payments that are made at a future date. The future value is defined by the specified rate of return or by the discount rate. If there is a fluctuation in regular payments then each of the cash flow is to be computed to get the future value of annuity. ### Explanation of Solution Formula to calculate future value of annuity is, FVAnnuity=PMT×((1+I)N×T1IT) (I) Where, • FV is future value of annuity. • PMT is periodic monthly payment. • I is interest rate. • N is number of periods. Substitute$400 for PMT 12% for I and 5 years for N and 2 for T.

FV=$400×((1+0 Expert Solution b. Summary Introduction To compute: Future value of annuity of$200 paid each 3 months for 5 years at a nominal rate of 12% compounded quarterly.

Future value of annuity: It states the value of regular payments that are made at a future date. The future value is defined by the specified rate of return or by the discount rate. If there is a fluctuation in regular payments then each of the cash flow is to be computed to get the future value of annuity.

Expert Solution

c.

Summary Introduction

To explain: The reason for annuity in part (b) is larger than annuity in part (a).

Future value of annuity: It states the value of regular payments that are made at a future date. The future value is defined by the specified rate of return or by the discount rate. If there is a fluctuation in regular payments then each of the cash flow is to be computed to get the future value of annuity.

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