Question

A financial planning service offers a unique program for parents to save for a child's college education. Starting on the child's 12th birthday, annual deposits are made. The first deposit is $5,000 and the required deposit increases by $1000 each year, until the child's 18th birthday, when the final deposit is made. Beginning on the child's 19th birthday, four annual withdrawals of $10,000 can be made. Assuming today is your child's 12th birthday, and assuming that you expect to earn a 6% annual return on your investments, analyze the proposed investment, and answer the questions below. Type your responses into the yellow boxes. 6% Discount Rate Present Value as of 12th birthday Deposit Amount Age (on birthday) Present Value as of 12th birthday Withdrawal amount 13 21 22 Total 25

please help me solve this problem with excel formulas please and thank you!!

Answer 1

a]

present value of each deposit = deposit amount / (1 + discount rate)ⁿ

where n = number of years after which the deposit is made

total present value of deposits = $45,963

b]

present value of each withdrawal = withdrawal amount / (1 + discount rate)ⁿ

where n = number of years after which the withdrawal is made

total present value of withdrawals = $24,428

c]

This is not a good investment as the total present value of withdrawals is lower than the total present value of deposits

PV of PV of 1 Age Deposit deposit withdrawal withdrawal 2 12 $ 5,000 $5,000 13 $ 6,000 $ 5,660 14 $ 7,000 $ 6,230 15 $ 8,000 $ 6,717 16 $ 9,000 $ 7,129 17 $ 10,000 $ 7,473 18 $ 11,000 $ 7,755 9 19 $ 10,000 $ 6,651 10 20 $ 10,000 $ 6,274 11 21 $ 10,000 $ 5,919 12 22 $ 10,000 $ 5,584 13 Total $ 45,963 $ 24,428

A B 1 Age Withdrawal PV of Withdrawal Deposit 5000 =B2+1000 =B3+1000 =B4+1000 =B5+1000 =B6+1000 =B7+1000 PV of deposit =B2/(1+6%)^(A2-12) =B3/(1+6%)^(A3-12) =B4/(1+6%)^(A4-12) =B5/(1+6%)^(A5-12) =B6/(1+6%)^(A6-12) =B7/(1+6%)^(A7-12) =B8/(1+6%)^(A8-12) 7 17 8 18 9 19 10 20 11 21 12 22 13 Total 10000 10000 10000 10000 =D9/(1+6%)^(A9-12) =D10/(1+6%)^(A10-12) =D11/(1+6%)^(A11-12) =D12/(1+6%)^(A12-12) =SUM(E2:E12) =SUM(C2:C12)

d]

No, the answer would not change.

At a discount rate of 4%, the total present value of withdrawals is still lower than the total present value of deposits

| AB Age Deposit PV of deposit withdrawal PV of withdrawal 12 $ 5,000 $ 5,000 13 $ 6,000 $ 5,769 14 $ 7,000 $ 6,472 15 $ 8,000 $ 7,112 16 $ 9,000 $ 7,693 17 $10,000 $ 8,219 18 $11,000 $ 8,693 19 $ 10,000 $ 7,599 20 $ 10,000 $ 7,307 $ 10,000 $ 7,026 $ 10,000 $ 6,756 Total $ 48,959 28,688 13

A B Withdrawal PV of Withdrawal 1 Age 2 12 3 13 4 14 Deposit 5000 =B2+1000 =B3+1000 =B4+1000 =B5+1000 =B6+1000 =B7+1000 PV of deposit =B2/(1+4%)^(A2-12) =B3/(1+4%)^(A3-12) =B4/(1+4%)^(A4-12) =B5/(1+4%)^(A5-12) =B6/(1+4%)^(A6-12) =B7/(1+4%)^(A7-12) =B8/(1+4%)^(A8-12) 5 15 6 16 7 17 8 18 9 19 10 20 11 21 12 22 13 Total 10000 10000 10000 10000 =D9/(1+4%)^(19-12) =D10/(1+4%)^(A10-12) =D11/(1+4%)^(A11-12) =D12/(1+4%)^(A12-12) =SUM(E2:E12) =SUM(C2:012)