Question

Challenge for you:

You deposit $400 each month into an account earning 5% annual interest compounded monthly.

a) How much will you have in the account in 20 years?
b) How much total money will you put into the account?
c) How much total interest will you earn?

Answer 1

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Answer:

a) $164,413.47

b) $96,000

c) $68,413.47

Explanation:

a) The account value is given by the annuity formula:

A = P(12/r)((1 +r/12)^(12·t) -1)

where monthly payment P earns interest at annual rate r compounded monthly for t years.

A = $400(12/0.05)((1 +0.05/12)^(12·20) -1) = $400(240)(1.712640285)

A ≈ $164,412.47

You will have $164,413.47 in the account after 20 years.

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b) You put $400 in the account each month for 240 months, for a total of ...

$400 × 240 = $96,000 . . . . total of your deposits

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c) The account balance in excess of your deposits is the amount of interest you earned:

$164,413.47 -96,000 = $68,413.47 . . . . interest earned