Question

Assume you plan to have a child 10 years from now. You expect that your child will enroll in a university at age 18 and graduate in 5 years. You want to have enough money once your child starts university to pay tuition of $75,000 from the account at the beginning of each year. You expect your child to receive a scholarship of $25,000 (paid in one lump sum) when they start university to put toward tuition. While your child is in university, the APR will be 8% compounded annually. If you can earn an APR of 12% compounded quarterly between now and when your child starts university how much total money would need to set aside today?

Answer 1

First lets calculate Amount required 28 years from now (i.e., at the start of college)

Present value = future value / (1+r)^n

r = rate of interest

n = number of periods

Present value = 75,000 + 75,000 / (1+8%) + 75000 / (1+8%)^2 + 75000 / (1+8%)^3 + 75,000 / (1+8%)^4

= 323409.51

Scholarship = 25,000

Net amount required = 323409.51 - 25000 = 298,409.51

Future value = Present value*(1+r)^n

r = 12% / 4 = 3%

n = number of periods = 28*4 = 112

298,409.51 = Present value*(1+3%)^112

Present value = 298409.51 / 27.40117

= 10,890.39

so we need to set aside $10,890.39 Today