Question

Dr Rice has reached his 70th birthday and is ready to retire. Dr. Rice has no formal finance training but has saved his money and invested carefully. Dr. Rice owns his house and the mortgage is paid off.

Dr. Rice has savings of $180,000. The investments are yielding 9 percent interest. Dr. Rice also has $12,000 in a savings account at 5% interest. Rice wants to keep the saving account level in real terms for emergencies.

Dr. Rice’s basic living expenses average about $1,500 per month and he plans to spend $500 a month on travel and hobbies.

To maintain this planned standard of living, Rice will rely on his investment portfolio. The interest on the portfolio is $16,200 per year (9 percent of $180,000) or $1,350 per month. Dr. Rice will also receive $750 per month in Social Security payments for the rest of his life. This payments are indexed for inflation. That is, the payments will automatically increase in proportion to changes in the consumer price index. Dr. Rice is concerned with inflation because although his Social Security payments increase with inflation, his portfolio interest will not increase.

Dr. Rice needs your advice. Dr. Rice thinks he will live 20 more years and is willing to use up all of his investment portfolio over that period. He also wants his monthly spending to increase with inflation. Can Dr. Rice afford his planned lifestyle in retirement? What would you advise Dr. Rice to do?

Assume that the investment portfolio continues to yield a 9 percent rate of return and that inflation will be 4 percent.

Answer 1

Let us roll to month n from now. Assuming payments are received at the beginning of the month,

• Interest income received from the investment portfolio is calculated as 0.75% of total investments. $180,000 is the initial portfolio, and it gets added by savings every month (after expenses). Hence, total interest income:

On solving, total interest income:

On further simplifying,

On further simplifying,

• Social security payments received (in $) (in case i is the inflation rate per month):

Henceforth, total monthly payments received (in $):

On simplifying, total monthly payments received (in $):

Total monthly spending is $2,000 per month at t = 0. Hence, total monthly spending (in $):

For Dr. Rice to afford,

On solving,

On solving, we obtain: -

Thus, Dr. Rice can afford his lifestyle till more than 240 months (20 years). For the purpose, I'd advise Dr. Rice to keep putting in the savings (after all his expenses) every month into his investment account that should yield him 9% rate of return.