Some friends of yours have just had a child. Thinking ahead, and realizing the p

Question

Some friends of yours have just had a child. Thinking ahead, and realizing the power of compound interest, they are considering investing for their child’s college education, which will begin in 18 years. Assume that the cost of a college education today is $150,000. Also assume there is no inflation and no tax on interest income used to pay college tuition and expenses.

Instruction: Round your answers to the nearest dollar.

a. If the interest rate is 5 percent, how much money will your friends need to put into their savings account today to have $150,000 in 18 years? They would need to put $ __________ into their savings account today.

b. What if the interest rate were 3 percent? They would need to put $ _________ into their savings account today.

c. The chance that the price of a college education will be the same 18 years from now as it is today seems remote. Assuming that the price will rise 4 percent per year, and that today’s interest rate is 6 percent, what will your friends' investment need to be? The amount of the investment would be $ _________ .

d. Return to the case with a 5 percent interest rate and no inflation (part a). Assume that your friends don’t have enough financial resources to make the entire investment at the beginning. Instead, they think they will be able to split their investment into two equal parts, one invested immediately and the second invested in five years. What is the amount of each part? The required size of the two investments would be $ _________.

Explanation / Answer

Answer 1 Future Value 150000 Period 18 years Interest Rate 5% Present Value=Future Value/(1+rate)^n Present Value=150000/(1+.05)^18 Present Value=150000/2.4066 Present Value=62328.1 Answer 2 Future Value 150000 Period 18 years Interest Rate 3% Present Value=Future Value/(1+rate)^n Present Value=150000/(1+.03)^18 Present Value=150000/1.7024 Present Value=88109.19 Answer 3 Collage expenses today 150000 Period 18 years Rate of rise in prices per year 4% Collage expenses after 18 years=150000*(1+.04)^18 Collage expenses after 18 years=150000*2.8005 Collage expenses after 18 years=420075 Present value of 420075=420075/(1+.06)^18 Present value of 420075=420075/2.8543 Present value of 420075=147172.7 Answer 4 Let his friends invest $x taday and $x after 5 years $150000=x(1.05)^18+x(1.05)^13 x=150000/(1.05)^18+(1.05)^13 x=150000/2.4066+1.8856 x=150000/4.2923 x=34946.3 Working on Future value factor Rate=5% Rate=3% Rate=4% Rate=6% 0 1 1 1 1 1 1.05 1.03 1.04 1.06 2 1.1025 1.0609 1.1024 1.1236 3 1.157625 1.092727 1.168544 1.191016 4 1.215506 1.125509 1.238657 1.262477 5 1.276282 1.159274 1.312976 1.338226 6 1.340096 1.194052 1.391755 1.418519 7 1.4071 1.229874 1.47526 1.50363 8 1.477455 1.26677 1.563775 1.593848 9 1.551328 1.304773 1.657602 1.689479 10 1.628895 1.343916 1.757058 1.790848 11 1.710339 1.384234 1.862482 1.898299 12 1.795856 1.425761 1.974231 2.012196 13 1.885649 1.468534 2.092684 2.132928 14 1.979932 1.51259 2.218245 2.260904 15 2.078928 1.557967 2.35134 2.396558 16 2.182875 1.604706 2.492421 2.540352 17 2.292018 1.652848 2.641966 2.692773 18 2.406619 1.702433 2.800484 2.854339

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