Response:
a) $639,610.76
b) $422,923.12
c) $0.00
d) $875,351.49
Clarification:
a) What deposit amount should she make today?
To determine this, we utilize the formula for calculating the present value of an ordinary annuity as follows:
PV = P × [{1 - [1 ÷ (1+r)]^n} ÷ r] …………………………………. (1)
Where;
PV = Amount to be deposited today =?
P = annual withdrawal = $95,000
r = interest rate = 4% = 0.04
n = total years = 8
Substituting the values into equation (1) provides:
PV = $95,000 × [{1 - [1 ÷ (1 + 0.04)]^8} ÷ 0.04]
PV = $95,000 × 6.73274487495041
PV = $639,610.76
Thus, she needs to deposit approximately $639,610.76 today.
b) What will the account balance be right after the third $95,000 withdrawal?
Note: Refer to Part A from the attached Excel document for this calculation.
This will show the ending balance at Year 3, which indicates $422,923.12.
c) What will the account balance be after all withdrawals, including the last one in 8 years?
Note: Also refer to Part A from the attached Excel document for this calculation.
The result will be the final balance at Year 8, showing $0.00.
d) Now, if you opt to drop out of school today and forgo all withdrawals while retaining your aunt’s deposit in the account accruing at 4.00%, what would your total be at the end of 8 years?
Note: See Part B from the attached Excel document for this calculation.
The total will be the closing balance at Year 8, which indicates $875,351.49.
The substantial amount arises because no withdrawals are made each year, allowing the principal to accumulate interest annually on the final balance.
