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Chapter 4, Problem 19RE
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### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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### 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 = $1000 , r = 4 % , t = 5 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$1000 is invested at the rate of 4% for 5 years:

 n 1 2 4 12 365 Continuous compounding A
Explanation

Given Information:

The amount of $1000 is invested at the rate of 4% for 5 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$1000 is invested at the rate of 4% for 5 years.

Here, P=$1000, r=4% and t=5 years. Simplify the rate as, r=4%=4100=0.04 When n=1, Substitute 1 for number of times compounded per year, 0.04 for interest rate,$1000 for the amount deposited and 5 years for the time in the formula, “A=P(1+rn)nt” as,

A=P(1+rn)nt=$1000(1+0.041)(1)(5) Solve further as, A=$1000(1.04)5$10001.21665$1216.65

When n=2,

Substitute 2 for number of times compounded per year, 0.04 for interest rate, $1000 for the amount deposited and 5 years for the time in the formula, “A=P(1+rn)nt” as, A=P(1+rn)nt=$1000(1+0.042)(2)(5)

Solve further as,

A=$1000(1.02)10$10001.21899$1218.99 When n=4, Substitute 4 for number of times compounded per year, 0.04 for interest rate,$1000 for the amount deposited and 5 years for the time in the formula, “A=P(1+rn)nt” as,

A=P(1+rn)nt=\$1000(1+0

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