Question

2. [9 points] Uncle Fred recently passed away and left $325,000 to his 50-year-old favorite niece. She immediately spent $100,000 on a town home but decided to invest the balance for her retirement at age 65. What rate of return must she earn on her investment over the next 15 years to permit her to withdraw $75,000 at the end of each year of her retirement through age 80 if her funds earn 10 percent annually during her retirement?

Answer 1

Inheritance passed on = $ 325,000

Amount Spent = $ 100,000

Amount to be invested = $ 225,000 .....(325000 - 100000)

For this problem, we need to first find out the investment value at her age of 65 which can sustain a $ 75,000 annual payout with balance earning 10% return. This can be done by using the Present Value calculation as given below:

Particulars		Calculator	Comments
Rate of Return	10%	I/Y	Rate of Return
No. of years	15	N	From Year 65 to 80
Yearly Withdrawal	75000	PMT	Withdrawal at end of year
Future Value	0.00	FV	Ending value of investment
Amount Required (PV)	570455.96	PV	Investment value at age of 65

Excel Calculations: = PV (10%, 15, -75000, 0.0, 0)

Calculator: The notations are given in the table above.

Hence, at the age of 65, she needs to accumulate $ 570455.96 to sustain her till age of 80.

Now we need to figure out at what rate of return the investable amount i.e. $ 225,000 can become $ 570455.96 in 15 years. The calculation is given below:

Particulars		Calculator	Comments
No. of years	15	N	From Year 50 to 65
Yearly Withdrawal	0	PMT	No Withdrawals
Future Value	570455.96	FV	Ending value of investment
Initial Investment	225000	PV	Starting value of investment
Rate of Return	6.40%	I/Y	Rate of Return

Excel Calculations: = Rate (15, 0, -225000, 570455.96, 0)

Calculator: The notations are given in the table above.

Hence, at a rate of return of 6.40%, her investment of $225,000 can give her $75,000 annual payment from her age of 65 to 80.

Answer is 6.40%