Question

The Thompson's want to send their two (2) year old son Johnny to College when he reaches the age of eighteen (18). They plan a four (4) year education program at a local college, where annual tuition is currently $9,000 Annually. They assume that college costs will increase at 5% & that they can earn 9% after-tax on their invested assets. How much do they need to set aside today to achieve this goal? a. $18,042.36 b. $17,473.55 c. $18,729.70 d. $18,423.37

Answer 1

Current College Fees = $9000

Johnny will start college after 16 years

College fees increases by 5% annually

Future Value of College Fees = College Fees Now *(1+i)ⁿ, where i is the increase in college fees per year and n is the number of years

First Year college fees = 9000*(1+0.05)¹⁶ = $19645.871
Second Year college fees = 9000*(1+0.05)¹⁷ = $20628.165
Third Year college fees = 9000*(1+0.05)¹⁸ = $21659.573
Fourth Year college fees = 9000*(1+0.05)¹⁹ = $22742.551

Present Value of Future Cash Flow = CF/(1+r)ⁿ

where, CF is the cash flow in Year n and r is the required rate of return

Hence, Investment Required today = 19645.871/(1+0.09)¹⁶ + 20628.165/(1+0.09)¹⁷ + 21659.573/(1+0.09)¹⁸ + 22742.551/(1+0.09)¹⁹ = $18729.702

Hence, (c) 18729.70 is the correct option