Chapter 4, Problem 22RE

### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

Chapter
Section

### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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# Finding Account Balances In Exercises 19-22, complete the table to determine the balance A for P dollars invested at rate r for t years, compounded n times per year. n 1 2 4 12 365 Continuous compounding A P = $4500 , r = 2 % , t = 25 years To determine To calculate: The amount A for corresponding value of n that is, number of times compounded per year in the following table when$4500 is invested at the rate of 2% for 25 years:

 n 1 2 4 12 365 Continuous compounding A
Explanation

Given Information:

The amount of $4500 is invested at the rate of 2% for 25 years and the table is as follows:  n 1 2 4 12 365 Continuous compounding A Formula used: The formula to compute the balance amount after t years when interest is compounded n times per year is, A=P(1+rn)nt Where, P is the deposited amount, A is the amount after t years, r is the interest rate in decimals, t is the number of years and n is the number of times compounded per year. The formula to compute the balance amount after t years when interest is compounded continuously is, A=Pert Where, P is the deposited amount, A is the amount after t years, r is the interest rate in decimals and t is the number of years. Calculation: Consider that the amount of$4500 is invested at the rate of 2% for 25 years.

Here, P=$4500, r=2% and t=25 years. Simplify the rate as, r=2%=2100=0.02 When n=1, Substitute 1 for number of times compounded per year, 0.02 for interest rate,$4500 for the amount deposited and 25 years for the time in the formula, A=P(1+rn)nt as,

A=P(1+rn)nt=$4500(1+0.021)(1)(25) Solve further as, A=$4500(1.02)25$45001.640606$7382.73

When n=2,

Substitute 2 for number of times compounded per year, 0.02 for interest rate, $4500 for the amount deposited and 25 years for the time in the formula, A=P(1+rn)nt as, A=P(1+rn)nt=$4500(1+0.022)(2)(25)

Solve further as,

A=$4500(1.01)50$45001.644632$7400.84 When n=4, Substitute 4 for number of times compounded per year, 0.02 for interest rate,$4500 for the amount deposited and 25 years for the time in the formula, A=P(1+rn)nt as,

A=P(1+rn)nt=\$4500(1+0

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