Chapter 9.2, Problem 83E

### Calculus

10th Edition
Ron Larson + 1 other
ISBN: 9781285057095

Chapter
Section

### Calculus

10th Edition
Ron Larson + 1 other
ISBN: 9781285057095
Textbook Problem

# Using a Geometric Series In Exercises 83-86, use the formula for the nth partial sum of a geometric series ∑ i = 0 n − 1 a r i = a ( 1 − r n ) 1 − r Present Value The winner of a $2,000,000) sweepstakes will be paid$100,000 per year for 20 years. The money earns 6% interest per year. The present value of the winnings is ∑ n = 1 20 100 , 000 ( 1 1.06 ) n . Compute the present value and interpret its meaning.

To determine

To calculate: The present value of the winning money and interpret its meaning when the winner of $2,000,000 sweepstakes will be paid$100,000 for 20 years with the interest rate of 6% per annum.

Explanation

Given:

When the winner of $2,000,000 sweepstakes will be paid$100,000 for 20 years with the interest rate of 6% per annum and the Present value of the winnings is n=120100000(11.06)n.

Formula used:

i=0n1ari=a(1rn)1r

Calculation:

Rewrite the series n=120100000(11.06)n as shown below:

n=120100000(11.06)n=100000(11.06)+100000(11.06)2+100000(11.06)20

S

The above series is a geometric series with a=100000(11.06),r=11.06 and n=20

So, compute the sum of the series n=120100000(11

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