Question

Suppose you invest $1,000 in an account paying 8% interest per year. a. What is the balance in the account after 3 years? How much of this balance corresponds to "interest on interest"? b. What is the balance in the account after 25 years? How much of this balance corresponds to "interest on interest"?

Answer 1

a. Balance after 3 years = Future Value

We use the formula:
A=P(1+r/100)^n
where
A=future value
P=present value
r=rate of interest
n=time period.

A = $ 1000 * (1+8/100)^3

= $ 1,259.712

Total Interest = A- P

= $ 1,259.712 - $ 1,000

= $ 259.712

Interest on Original Balance = Principal * Interest Rate * Time

= $ 1,000 * 8%* 3

= $ 240

Interest on Interest = Total Interest - Interest on Original Balance

= $ 259.712- $ 240

= $ 19.712

Answer: $ 1,259.712 and $ 19.712

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b.

Balance after 25 years = Future Value

We use the formula:
A=P(1+r/100)^n
where
A=future value
P=present value
r=rate of interest
n=time period.

A = $ 1000 * (1+8/100)^25

= $ 6,848.475196

= $ 6,848.48

Total Interest = A- P

= $ 6,848.475196 - $ 1,000

= $ 5,848.475196

Interest on Original Balance = Principal * Interest Rate * Time

= $ 1,000 * 8%* 25

= $ 2,000

Interest on Interest = Total Interest - Interest on Original Balance

= $ 5,848.475196- $ 2,000

= $ 3,848.475196

= $ 3,848.48

Answer: $ 6,848.48 and $3,848.48