Question

A young couple wants to have a college fund that will pay $40,000 at the end of each half-year for 8 years. (a) If they can invest at 8%, compounded semiannually, how much do they need to invest at the end of each 6-month period for the next 18 years to begin making their college withdrawals 6 months after their last investment? (Round your answer to the nearest cent.) $ (b) Suppose 8 years after beginning the annuity payments, they receive an inheritance of $38,000 that they contribute to the account, and they continue to make their regular payments as found in part (a). How many college withdrawals will they be able to make before the account balance is $0? (Round your answer to the nearest whole number.) withdrawals

Answer 1

a) Let's calculate the amount they need at end of 18 years using PV function

N = 8 x 2 = 16, I/Y = 8%/2 = 4%, PMT = 40,000, FV = 0

=> Compute PV = $466,091.82

In order to accumulate the above sum, semi-annual payment can be calculated using PMT function

N = 18 x 2 = 36, PV = 0, FV = 466,091.82, I/Y = 4%

=> Compute PMT = $6,006.47

b) Value of the inheritance 8 years later = 38,000 x (1 + 4%)^16 = $71,173.29

Total amount available for college = $71,173.29 + $466,091.82 = $537,265.11

No. of withdrawals can be calculated using N function

I/Y = 4%, PV = 537,265.11, FV = 0, PMT = -40,000

=> Compute N = 19.65 periods = 20 withdrawals