Question

Calculate the amount of money that must be deposited at the end of every three months into an account paying 6% compounded monthly to accumulate to $12 500.00 in ten years?

Answer 1

There are 12 months in a year.

There are 4 quarterly periods in a year.

(1 + monthly)^n - 1 = (1 + quarterly rate)^n - 1

(1 + 0.06/12)^12 - 1 = (1 + quarterly rate)^4 - 1

(1 + 0.005)^12 - 1 = (1 + quarterly rate)^4 - 1

1.06168 - 1 =  (1 + quarterly rate)^4 - 1

1.06168 = (1 + quarterly rate)^4

1.01508 = 1 + quarterly rate

quarterly rate = 0.01508 or 1.508%

Number of periods = 10 * 4 = 40

Future value = Quarterly payments * [(1 + rate)^time - 1] / rate

12,500 = Quarterly payments * [(1 + 0.01508)^40 - 1] / 0.01508

12,500 = Quarterly payments * [1.81975 - 1] / 0.01508

12,500 = Quarterly payments * 54.35983

Quarterly payments = $229.95