Question

At age 65, Kim has $950,000 in her retirement fund. How much she can withdraw each month until age 90 completely depleting her fund? Assume an interest rate of 7.5%.

(a) $7,020.42 (b) $1,082.92 (c) $85,225.14 (d) $59,375.00 (e) none of the above

An employee plans to participate in their company pension plan. The employee would like to accumulate $1,500,000 over the next 35 years. The current rate is 6.4% per year com- pounded quarterly. Which formulas would you use to find how much the employees quarterly deposits should be in order to reach his goal?

**Please answer both questions**

Answer 1

Solution 1:

Annual interest rate = 7.50%, Monthly rate = 0.625%

Balance in fund at age of 65 = $950,000

Balance at age of 90 will be nil, therefore life of fund = 25 years

Total nos of monthly installment that will be drawn by Kim = 25*12 = 300

Let amount of monthly withdrawl is X.

Therefore present value of X at 0.625% will be equal to $950,000

Therefore

X * cumulative PV factor at 0.625% for 300 periods = $950,000

X * 135.319613 = $950,000

X = $7,020.42

Hence option a is correct.

Solution 2:

Future value of annuity = $1,500,000

Period = 35 years, 140 quarterly periods

Interest rate = 6.4%, Quarterly rate = 1.60%

Let quarterly deposit at the end of each quarter = X

Furture value of annuity = P [(1+r)^n-1/r]

X [(1.016)^140 -1 / 0.016] = $1,500,000

X * (9.228245-1/0.016) = $1,500,000

X = $2,916.78