Chapter 02, Problem 139 You decide to open a retirement account at your local ba

Question

Chapter 02, Problem 139 You decide to open a retirement account at your local bank that pays 7%/year/month (7% per year compounded monthly). For the next 20 years, you will deposit $300 per month into the account, with all deposits and withdrawals occurring at month's end. On the day of the last deposit, you wil retire. Your expenses during the first year of retirement will be covered by your company's retirement plan. As such, your first withdrawal from your retirement account will occur on the day exactly 12 months after the last deposit Click here to access the TVM Factor Table Calculator What monthly withdrawal can you make if you want the account to last 25 years? $ Round entry to the nearest dollar. Tolerance is ±4. What monthly withdrawal can you make if you want the account to last forever (with infinite withdrawals)? $ Round entry to the nearest dollar. Tolerance is ±4.

Explanation / Answer

Monthly (nominal) interest rate = 7%/12 = 0.5833

Number of months = 20 x 12 = 240

Future worth after 20 years ($) = 300 x F/A(0.5833%, 240) = 300 x 520.9564** = 156,286.93

(a) Number of months = 12 x 25 = 300

Monthly withdrawals ($) = 156,286.93 / P/A(0.5833%, 300) = 156,286.93 / 141.4881** = 1105

(b) Monthly withdrawal ($) = 156,286.93 x 0.005833 = 912

**F/A(r%, N) ] [(1 + r)N - r] / r

F/A(0.5833%, 240)] = [(1.005833)240 - 1] / 0.005833 = (4.0387 - 1) / 0.005833 = 3.0387 / 0.005833

= 520.9564

**P/A(r%, N) = [1 - (1 + r)-N] / r

P/A(0.5833%, 300) = [1 - (1.005833)-300] / 0.005833 = (1 - 0.1747) / 0.005833 = 0.8253 / 0.005833

= 141.4881

Related Questions

Navigate

• Browse (All)
• Browse C
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.