Chapter 5, Problem 25P

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14th Edition

Eugene F. Brigham + 1 other

ISBN: 9781285867977

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?

**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

Formula to calculate future value of annuity is,

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.

**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.

**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.

Ch-5 P-3PCh-5 P-4PCh-5 P-5PCh-5 P-6PCh-5 P-7PCh-5 P-8PCh-5 P-9PCh-5 P-10PCh-5 P-11PCh-5 P-12PCh-5 P-13PCh-5 P-14PCh-5 P-15PCh-5 P-16PCh-5 P-17PCh-5 P-18PCh-5 P-19PCh-5 P-20PCh-5 P-21PCh-5 P-22PCh-5 P-23PCh-5 P-24PCh-5 P-25PCh-5 P-26PCh-5 P-27PCh-5 P-28PCh-5 P-29PCh-5 P-30PCh-5 P-31PCh-5 P-32PCh-5 P-33PCh-5 P-34PCh-5 P-35PCh-5 P-36PCh-5 P-37PCh-5 P-38PCh-5 P-39PCh-5 P-40PCh-5 P-41SPCh-5 P-42IC

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