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Question 3 Highlander, an immortal, wants to retire in 25 years. His pension fund manager suggests...

Question 3 Highlander, an immortal, wants to retire in 25 years. His pension fund manager suggests that he contribute $500 per month for the next 25 years towards his retirement pension fund. Once he retires, he will receive $750 per month in perpetuity as his pension. What is the APR (compounded monthly) that his pension fund manager is using?

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Answer #1

Let APR = r

Investment per month P = $500

Investment period = 25*12 = 300

Interest rate = r/12 monthly

Hence, Total Amount at end of 25 years = P[(1+r)n -1]/r = 500[(1+r/12)25 -1]/(r/12)

After retirement X = $750 in perpetuity is received

Hence, value of the perpetuity at retirement = X/r = 750/(r/12)

Hence, the value of investment at time of retirement = value of perpetuity at time of retirement

=> 500[(1+r/12)300 -1]/(r/12) = 750/(r/12)

=> r = 0.0367 or 3.67%

Hence APR = 3.67%

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