   Chapter 9.1, Problem 68E

Chapter
Section
Textbook Problem

# Compound Interest A deposit of $100 is made in an account at the beginning of each month at an annual interest rate of 3% compounded monthly. The balance in the account after n months is A n = 100 ( 401 ) [ ( 1.0025 ) n − 1 ] .(a) Compute the first six terms of the sequence { A n } .(b) Find the balance in the account after 5 years by computing the 60th term of the sequence.(c) Find the balance in the account after 20 years by computing the 240th term of the sequence. (a) To determine To calculate: The first six terms of the sequence {An} if Principal amount is$100 and the rate of interest is 3%. The balance in the amount after n months is An=100(401)[(1.0025n)1].

Explanation

Given:

Principal amount is \$100 and the rate of interest is 3%. The balance in the amount after n months is An=100(401)[(1.0025n)1].

Calculation:

Consider the account balance,

An=100(401)[(1.0025n)1]

The first six terms of this sequence are,

For n=0.

A0=100(401)[(1.00250)1]=0

In the first month,

A1=100(401)[(1.00251)1]=100.25

In the second month,

A2=100(401)[(1.00252)1]=200

(b)

To determine

To calculate: The balance in the account after 5 years.

(c)

To determine

To calculate: The balance in the account after 20 years.

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