Suppose that a family wants to start a college fund for their child. If they can get a rate of 5.2%, compounded monthly, and want the fund to have a value of $55,500 after 20 years, how much should they deposit monthly? Assume an ordinary annuity and round to the nearest cent.

The answer is $135.40

The formula for ordinary annuity is:

P = A * ((1 + r) ⁿ - 1) / r

P - future value

r - rate

A - annuity payment

n - the number of years

P = $55,000

r = 5.2% = 0.052

n = 20 years

55000 = A ((1 + 0.052) ²⁰ - 1) / 0.052

55000 = A * ((1.052) ²⁰ - 1) / 0.052

55000 = A * (2.76 - 1) / 0.052

55000 = A * 1.76 / 0.052

55000 = A * 33.85

A = 55000 / 33.85

A = 1624.82

This is annual payment, and since year has 12 months, monthly payment is

1624.82 / 12 = $135.40