Chapter 5, Problem 19P

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15th Edition

Eugene F. Brigham + 1 other

ISBN: 9781337395250

Textbook Problem

**FUTURE VALUE OF AN ANNUITY** Your client is 26 years old. She wants to begin saving for retirement, with the first payment to come one year from now. She can save $8,000 per year, and you advise her to invest it in the stock market, which you expect to provide an average return of 10% 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 earn 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 the annuity which has repeating payment and which takes place at the beginning of each period. Under annuity due, the time interval of payment and the amount remains the same. An ordinary annuity has lesser present value than the annuity due, as the payment made in ordinary annuity is at the end of the period while in annuity due is at the beginning of the period.

Explanation

Formula to calculate future value of annuity,

Where,

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

Substitute $8,000 for C, 10% for I and 39

**b.**

Summary Introduction

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

**Annuity Due:**

Annuity due is the annuity which has repeating payment and which takes place at the beginning of each period. Under annuity due, the time interval of payment and the amount remains the same. An ordinary annuity has lesser present value than the annuity due, as the payment made in ordinary annuity is at the end of the period while in annuity due is at the beginning of the period.

**c.**

Summary Introduction

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

**Annuity Due:**

Annuity due is the annuity which has repeating payment and which takes place at the beginning of each period. Under annuity due, the time interval of payment and the amount remains the same. An ordinary annuity has lesser present value than the annuity due, as the payment made in ordinary annuity is at the end of the period while in annuity due is at the beginning of the period.

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