Chapter 13.CR, Problem 64E

### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742

Chapter
Section

### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742
Textbook Problem

# Annuity Find the amount of an annuity consisting of 16 annual payments of $1000 each into an account pays 8 % interest per year, compounded annually. To determine To find: The amount of an annuity. Explanation Given: 16 annual payments of$1000 each are deposited into an account that pays 8% interest per year, compounded annually.

Approach:

Show that the future value of $1000 payments in subsequent years forms a geometric sequence and find the partial sum of this geometric sequence. Calculation:$1000 payment at the end of first year is compounded annually at 8% interest for next 15 years. So the future value of this payment is 1000(1+8/100)15=1000(1.0815).

$1000 payment at the end of second year is compounded annually at 8% interest for next 14 years. So the future value of this payment is 1000(1+8/100)14=1000(1.0814).$1000 payment at the end of third year is compounded annually at 8% interest for next 13 years. So the future value of this payment is 1000(1+8/100)13=1000(1

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