Question #264180

John Anderson wants to save for his daughterâ€™s college tuition. He will have to pay Rs. 50,000 at the end of each year for the four years that her daughter attends college. He has 8 years until his daughter starts college to save up for her tuition. Using a 7% interest rate compounded annually, the amount Anderson would have to save each year for 8 years is closest to:

Expert's answer

**Solution:**

First, calculate the present value of an annuity for the school fees required:

PV = PMT "\\times " [1 â€“ (1 + r)^{-n} "\\div " r]

PV = 50,000 "\\times " [1 â€“ (1+0.07)^{-4}"\\div " 0.07] = 50,000 "\\times " 3.3872 = 169,360

PV = 169,360

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Now calculate the periodic payments of FV:

P = FV"\\div " [(1+r)^{n} â€“ 1"\\div " r] = 169,360"\\div " (1+0.07)^{8} â€“ 1"\\div " 0.07] = 169,360"\\div " 10.2598 = 16,507

The amount Anderson would have to save each year for 8 years is closest to Rs. 16,500

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