Question #264180

John Anderson wants to save for his daughter’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 – (1 + r)^{-n} "\\div" r]

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

PV = 169,360

Now calculate the periodic payments of FV:

P = FV"\\div" [(1+r)^{n} – 1"\\div" r] = 169,360"\\div" (1+0.07)^{8} – 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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