The Financial Advisor is a weekly column in the local newspaper. Assume you must

Question

The Financial Advisor is a weekly column in the local newspaper. Assume you must answer the following question. Ac€A?I recently retired at age 65, and I have a tax-free retirement annuity coming due soon. I have three options. I can receive (A) $30,976 now, (B) $359.60 per month for the rest of my life, or (C) $513.80 per month for the next 10 years. What should I do?Ac€?? Ignore the timing of the monthly cash flows and assume that the payments are received at the end of year. Assume the 10-year annuity will continue to be paid to loved heirs if the person dies before the 10-year period is over. (a) (10 points) If interest rate i = 6%, develop a choice table for lives from 5 to 30 years. (You do not know how long this person or other readers may live.) (b) (5 points) If i = 10%, develop a choice table for lives from 5 to 30 years. (You do not know how long this person or other readers may live.) (c) (5 points) How does increasing the interest rate change your recommendations?

Explanation / Answer

This is a case of evaluating present value for different available options.

Let's calculate PV for life long annuity.

Receiving 359.6 per month equals 4315.2 per year.

Hence PV = 4315.2/i + 4315.2/i^2 + .....

This simplifies to 4315.2/i = 71920 if i = 6% and = 43152 if i = 10%.

In option C where annuity is for 10 years, n in previous formula will range from 1 to 10.

Amount per year = 513.8*12 = 6165.6

At 6% rate, PV of this becomes 45380 and at 10% rate 37885.

Hence option B at 6% rate is the best option, which gives highest PV.

Coming to the 2nd part where table has to be developed, the system will act as annuity if person dies before 10 years and post that it becomes a perpetuity.

Annuity formula is summation of P/(1+i)^n, where P is amount = 6165.6, i is rate 6% or 10% and n is years.

Hence, perpetuity is 102760 if rate is 6% and 61656 if rate is 10%.

Best Amount is received when the person dies at end of 10 years and heirs get perpetuity for life long.

As the rate increases, PV reduces and hence best benefit is received for lower rates.

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