Please show the steps to get to the answer provided. Thank you. A couple\'s daug
ID: 1143501 • Letter: P
Question
Please show the steps to get to the answer provided. Thank you.
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.
The Answer was: 1,664
Explanation / Answer
The answer is as follows:
The annual compound rate = 15 %
Quarterly rate = 3.75 % = 0.0375
Rate of inflation = 10 %
Thus, at the end of 18 years the amount that must be accumulated = 17000 [ 1 + 1/1.1 + 1 / 1.1^2 + 1 / 1.1^3 ] = 59276
Now, let the amount to be invested every quarter be P
P(1.0375) + P (1.0375)^2 + . . . .. + P(1.0375)^44 = 112.1096 P
Now this hs to be discounted at 10 % inflation rate for 11 years i.e 1.10 ^11 = 3.138
Thus, 112.1096 P/ 3.14 = 35.6 P
35.6 P = 59276
P = 59276 / 35.6 = 1665.05 $
Which can be rounded off to 1665 $
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