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 $ _____.

With the 5% interest rate, they need to put $X into their saving account today in order to get $150,000 in 18 years, with X is calculated by applying the formula for calculating future value is below:

X * (1+5%)^18 = 150,000 <=> X = 150,000 / (1+5%)^18 = $62,328.10

b.

With the 3% interest rate, they need to put $X into their saving account today in order to get $150,000 in 18 years, with X is calculated by applying the formula for calculating future value is below:

X * (1+3%)^18 = 150,000 <=> X = 150,000 / (1+3%)^18 = $88,109.19

c.

The tuition fee is 18 years will be: 150,000 * (1+4%)^18 = $303,872.50

With the 6% interest rate, they need to put $X into their saving account today in order to get $303,872.5 in 18 years, with X is calculated by applying the formula for calculating future value is below:

X * (1+6%)^18 = 303,872.5 <=> X = 303,872.5 / (1+6%)^18 = $106,459.84.

d.

Denote X is the amount of investment in each equal investment. The sum of future value of the two investment compounding at 5% must be equal to the tuition fee of $150,000, we have the calculation as below:

X * ( 1+5%)^18 + X * (1+5%)^(18-5) = 150,000 <=> 4.29227 * X = 150,000 <=> X = $34,946.54