Suppose that a family wants to start a college fund for their child. If they can get a rate of 7.5%, compounded monthly, and want the fund to have a value of $75,000 after 18 years, how much should they deposit monthly? Assume an ordinary annuity and round to the nearest cent.

For an ordinary annuity, the future value is the monthly deposit multiplied by ((1 + i)^n − 1) / i. Here, the monthly rate is 0.075 / 12 = 0.00625, and there are 18 × 12 = 216 deposits. Solving for the deposit gives $75,000 × 0.00625 / ((1.00625)^216 − 1) ≈ $164.98 per month, so the correct choice is $164.98.

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