Question

Laurie Campbell deposits $3,000 at the end of each quarter in an account paying 8% interest compounded quarterly. How many years will it take for her to have $60,000 in her account?

Answer 1

The number of years is computed as shown below:

Future value = Quarterly payment x [ [ (1 + r)ⁿ – 1 ] / r ]

r is computed as follows:

= 0.08 / 4

= 2% or 0.02

$ 60,000 = $ 3,000 x [ [ (1 + 0.02)ⁿ - 1 ] / 0.02 ]

20 x 0.02 = 1.02 ⁿ - 1

0.4 = 1.02 ⁿ - 1

1.4 = 1.02 ⁿ

Taking log both sides, we shall get

log 1.4 = n log 1.02

0.336472237 = n x 0.019802627

n = 0.336472237 / 0.019802627

n = 16.99129272

Now since the interest is compounded quarterly, we need to multiply the above figure by 4.

So,

n = 16.99129272 x 4

= 67.9652 years Approximately

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