Chapter 13.CR, Problem 65E

### 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

# Investment How much money should be invested every quarter at 12 % per year, compounded quarterly, in order to have $10000 in one year? To determine To find: Money to be invested every quarter. Explanation Given: Interest rate is 12%. Target amount at the end of year is$10,000.

Approach:

Show that quarterly payment compounded quarterly form a geometric sequence and solve for the quarterly payment using the given target amount.

Calculation:

Let $x be the quarterly payment. Effective quarterly interest rate is r=12/4=3%$x payment at the end of first quarter is compounded quarterly at 3% interest for next 3 quarters. So the future value of this payment is x(1+3/100)3=x(1.033).

$x payment at the end of second quarter is compounded quarterly at 3% interest for next 2 quarters. So the future value of this payment is x(1+3/100)2=x(1.032).$x payment at the end of third quarter is compounded quarterly at 3% interest for next 1 quarter. So the future value of this payment is x(1+3/100)=x(1.03).

\$x payment at the end of the year has the future value of x

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