Answer:
a) $639,610.76
b) $422,923.12
c) $0.00
d) $875,351.49
Explanation:
a) How large of a deposit must she make today?
To calculate this, we make us of 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 deposit today =?
P = yearly withdrawal = $95,000
r = interest rate = 4% = 0.04
n = number of years = 8
Substitute the values into equation (1) to have:
PV = $95,000 × [{1 - [1 ÷ (1 + 0.04)]^8} ÷ 0.04]
PV = $95,000 × 6.73274487495041
PV = $639,610.76
Therefore, she must make a deposit of approximately $639,610.76 today.
b) How much will be in the account immediately after you make the 3rd $95,000 withdrawal
Note: See Part A in the attached excel file for the calculation of this.
The answer is the ending balance in Year 3 and it can be seen that this is $422,923.12.
c) How much will be in the account immediately after you make all the withdrawals including the last one in 8 years?
Note: Also see Part A in the attached excel file for the calculation of this.
The answer is the ending balance in Year 8 and it can be seen that this is $0.00.
d) Now, if you decide to drop out of school today and not make any of the withdrawal, but instead keep your aunt’s money, that she deposited today, in the account that is earning 4.00%, how much would you have at the end of 8 years?
Note: See Part B in the attached excel file for the calculation of this.
The answer is the ending balance in Year 8 and it can be seen that this is $875,351.49.
The amount is that large because zero amount is withdrawn each year while the account kept on earning interest yearly on the ending balance.
