Question

Suppose a certain manufacturer deposits $7,000 at the beginning of each 3 month period for 8 years in an account paying 8% interest compounded quarterly.

Required:
a. How much (in $) will be in the account at the end of the 6 year period?
b. What is the total amount (in $) of interest earned in this account?

Answer 1

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Answer:

a) $217,212.10 after 6 years

b) $91,780.99 interest earned

Explanation:

The future value of this "annuity due" can be found using the formula ...

FV = P(1 +n/r)((1 +r/n)^(nt) -1)

where P is the periodic payment made n times per year and r is the annual interest rate.

a) After 6 years, the value of the account is ...

FV = $7000(1 +4/0.08)((1 +0.08/4)^(4·6) -1) = $217,212.10 . . . . 6-yr balance

__

b) After 8 years, the value in the account is ...

FV = $7000(51)(1.02^32 -1) = $315,780.99

The total of payments is $7000×32 = $224,000, so the interest earned is ...

I = $315,780.99 -224,000 = $91,780.99 . . . interest earned