Question

Jane would like to start saving for the college education of newborn, Matthew, who is a month old. She decided to send Matthew to Harvard and estimate that the currently it cost $15,000 per year in today’s dollar for tuition. They assume that Matthew will have 4-year college education starting at age 18. The investment rate of return for the savings plan is 8%. Education inflation is expected to be 6% annually. Calculate how much they will need save annually in order to fulfill Mark’s education goal.

Answer 1

Cost of education after 18 year at 6% rate = 15000(1.06)^18 = $42815.09

after 19th year = 42815.06*1.06 = $45383.99

after 20th year = 42815.06*1.06^2 = $48107.03

after 21st year = 42815.06*1.06^3 = $50993.45

Now, find the PV at 18th for all the Future values:

At 18th year, PV of 19th year = $45383.99/1.08 = $42022.21

At 18th year, PV of 20th year = $45383.99/1.08 = $41244.02

At 18th year, PV of 21st year = $45383.99/1.08 = $40480.24

Total corpus required at 18th year would be = $42815.09+$42022.21+$41244.02+$40480.24 = $166561.57

Money which is needed to save annually to get $166561.57 after 18 years is :

x/1.08 + x/1.08^2 + ....................................x/(1.08^18) = $166561.57

x = $4447.54