   Chapter 11.1, Problem 66E

Chapter
Section
Textbook Problem

# If you deposit $100 at the end of every month into an account that pays 3% interest per year compounded monthly, the amount of interest accumulated after n months is given by the sequence I n = 100 ( 1.0025 n − 1 0.0025 − n ) (a) Find the first six terms of the sequence. (b) How much interest will you have earned after two years? (a) To determine To find: The first five terms of the sequence. Explanation Given: The sequence is In=100((1.0025)n10.0025n) . (1) Calculation: Obtain the first term of the sequence by substituting 1 for n in equation (1). I1=100((1.0025)110.00251)=100(1.002510.00250.0025)=100(00.0025)=0 Thus, the first termof the sequence is I1=$0 .

Obtain the second term of the sequence by substituting 2 for n in equation (1).

I2=100((1.0025)210.00252)=100(0.005006250.00252)=100(2.00252)=0.25

Thus, the second term of the sequence is I2=$0.25 . Obtain the third term of the sequence by substituting 3 for n in equation (1). I3=100((1.0025)310.00253)=100(0.007518770.00253)=100(3.0075083)=0.75 Thus, the third term of the sequence is I3=$0.75 .

Obtain the fourth term of the sequence by substituting 4 for n in equation (1).

I4=100((1

(b)

To determine

To find: The amount of interest earned after two years.

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