A couple\'s daughter has just turned seven. They want to set up a savings plan w

Question

A couple's daughter has just turned seven. They want to set up a savings plan whereby each quarter they deposit an amount at 15% compounded quarterly to cover the cost of her college when their daughter turns 18. They estimate that an amount of 17,000 per year in today's dollars will be required for each of the four years of college. (Assume that the 17,000 amounts are paid out on the daughter's birthdays, starting with her 18th birthday.) The inflation rate is assumed to be 10% per year. Determine the uniform quarterly payments that are required if the last payment is made on the daughter's 18th birthday. Enter your answer to the nearest whole number.

Explanation / Answer

In such problems we can calculate all the values to a fixed point in future.

Here, our point of reference can be the 18th birthday of the girl.

Inflation rate = 10% and the amount required on each birthday starting from her 18th birthday = 17,000

Thus, net amount that the couple must have on the 18th birthday =

17000 + 17000(1.10) + 17000(1.10)^2 + 17000 (1.10)^3 = 78880

Now the instalments are quarterly in nature. In 11 years , 44 instalments shall be paid.

Rate of interest = 15% per annum = 15 / 4 = 3.75 % per quarter

Let the quarterly payment made be P:

We assume that the first instalment is paid on the 7th birthday itself

Thus, P(1+i)^44 + P(1+i)^43+ P(1+i)^42 + . . . . .. + P(1+i) = 78880

Thus, P(1+i) [ (1+i)^44 - 1 ] / [(1+i) - 1 ] = 78880

i = 0.0375

Substituing the value of i we have:

112.1096 P = 78880

P = 703.59 $ must be saved every quarter.

Note: If the first payment is made after the birthday at the end of three months, then amount to be saved per quarter would be: 730 $

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