Question

College Problem ther and mother are planning a savings program to put their daughter through college. Their mer is now 4 years old. She plans to enroll at the university when she is 18 and it should take her 4 years to complete her education. Currently, the cost per year (for tuition, etc.) is $12,000, but a 370 ation rate in these costs is forecasted. The cost for each year of college will be withdrawn when she turns 18, 19, 20, and 21. m The daughter received $20,000 today from her grandmother; this money, which is invested in an account paying 6% interest compounded annually, will be used to help meet the cost of the daughter's education. The rest of the costs will be met by money the parents will deposit in the savings account. They will make 10 equal annual deposits to the account, with the first deposit being made today on her 4th birthday and the last one being made on her 13th birthday. These deposits will also earn 6% interest compounded annually. How large must each deposit (from the parents) be in order to put the daughter through college? (Round cash flows to nearest dollar throughout). a. $891 b. $926 C. $1,064 d. $1,183 e. $1,381

Answer 1

Amount required on 18^th birthday is equal to present value of all future withdrawals

= 12000(1.03)^14 + 12000(1.03)^15/(1.06) + 12000(1.03)^16/(1.06)^2 + 12000(1.03)^17/(1.06)^3

= $69,579.79

Amount required on 13^th birthday = 69,579.79/(1.06)^5

= $51,994.07

Value of 20,000 on 13^th birthday = 20,000(1.06)^9 = $33789.58

Additional amount required = $18204.49

Let annual deposits be x

Future value of annuity = *x[{(1.06)^10 – 1}/0.06]

18204.49 = 13.1807949x

X = $1,381.14

Hence, the answer is e. $1381