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

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