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

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.

Instructions: Enter your responses rounded to the nearest dollar.

a. If the interest rate is 3 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 7 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 8 percent, what will your friends' investment need to be?

The amount of the investment would be $ .

d. Return to the case with a 3 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 $ .

Solutions

Expert Solution

(a)
Interest Rate is 3%
Funds require at the beginning of 18th year is $150,000 (i.e. at the end of 17th year)
Funds to be put into savings as on today is as follows
	=	1,50,000
	=	PVIFA (3%, 17)

	=	$90752.47

(b)
Interest Rate is 7%
Funds to be put into savings as on today is as follows
	=	1,50,000
	=	PVIFA (7%, 17)

	=	$47486.16

c)
Inflation rate is 4% per yr
Interest Rate is 8%
Funds to be put into savings as on today is as follows

	=	150000* (1.04)¹⁷
	=	PVIFA (8%, 17)

	=	$ 78,968.55

d)
Interest Rate is 3%
Assuming that the second part of investment in 5 yrs means from end of 1st yr to 5th years
Since the investment in part 1 (i.e. immediately) and 2nd part (i.e. investment in 5 yrs) is same
Assume that the investment to be made from 1st to 5th yr is a
Hence total investment in second part is 5a
Hence investment in part 1 is also 5a

Now lets find out the value of a

150,000 = 5a(1.03)¹⁷ + a(1.03)¹⁶ + a(1.03)¹⁵ + a(1.03)¹⁴ + a(1.03)¹³ + a(1.03)¹²
150000 = 15.83a
a= 9475.68

Hence investment would be as follows
Part 1- immediately= 5*9475.68 = 47378.40
Part 1- in 5 years is $9475.68 each for 5 years

jeff jeffy answered 1 month ago

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