Chapter 5, Problem 19P

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14th Edition

Eugene F. Brigham + 1 other

ISBN: 9781285867977

Textbook Problem

**FUTURE VALUE OF AN ANNUITY** Your client is 40 years old. She wants to begin saving for retirement with the first payment to come one year from now. She can save $5,000 per year, and you advise her to invest it in the stock market, which you expect to provide an average return of 9% in the future.

- a. If she follows your advice, how much money will she have at 65?
- b. How much will she have at 70?
- c. She expects to live for 20 years if she retires at 65 and for 15 years if she retires at 70. If her investments continue to cam the same rate, how much will she be able to withdraw at the end of each year after retirement at each retirement age?

**a.**

Summary Introduction

**To compute:** Future value of ordinary annuity at the age of 65.

**Annuity Due:** Annuity due is that annuity, which has repeating payment that occurs at the beginning of each period. Under annuity due, time interval of payment and amount is to be remaining same. An ordinary annuity has lesser present value than annuity due, as payment made in ordinary annuity is at the end of the period, while in annuity due, it is at the beginning of the period.

Explanation

**Solution:**

Formula to calculate future value of annuity,

Where,

- FV is future value.
- C is monthly payment.
- I is interest rate.
- N is number of years.

Substitute $5,000 for C, 9% for I and 25

**b.**

Summary Introduction

**To compute:** Future value of ordinary annuity at the age of 70.

**c.**

Summary Introduction

**To compute:** Monthly payment of mortgage for 20 years and 15 years.

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