Question

Assume that you will retire in 30 years. You plan to be retired for a total of 30 years. You wish to withdraw the equivalent of $50,000 per year (in TODAY'S dollars) from your retirement fund each year that you are retired (ASSUME that there will NOT be any adjustments for inflation DURING your retirement. You will withdraw the same dollar amount every year that you are retired). The expected inflation rate for the next 30 years is 3%. You can earn 10% on your investments prior to retirement and you plan to earn 7% on your investments during retirement. How much do you need to invest each month (beginning right now) in order to be able to afford to retire?

$919

$454

$666

$877

You are trying to choose between two investments:

A - Invest $2,400 per year for 10 years, earning an 8% annual rate of interest. OR,

B - Invest $200 per month for 10 years, earning 8% annual rate of interest.

Which of the following is most correct?

There is no way to tell which investment has the higher future value.

Investment A has the higher future value.

Investment B has the higher future value.

Investments A and B have identical future values.

Answer 1

Amount to be withdrawan each year from the retirement fund = 50,000(1.03)³⁰

= $121,363.12

Amount required on the day of retirement = 121,363.12*PVAF(7%, 30 years)

= 121,363.12*12.409

= $1,505,995

Let the amount deposited each month be x

X*[{(1+0.10*1/12)³⁶⁰-1}/0.0083333] = 1,505,995

2260.488x = 1,505,995

X = 666.22

Hence, amount required to be deposited each month = $666

Investment B has the higher future value,

Since the compounding will be done monthly and hence, will provide higher effective rate of interest

Future value of investment A = 2,400[{(1.08) ¹⁰ – 1}/0.08] = $34,767.75

Investment B = [{“200(1.0066667)¹²⁰-1}/0.0066667] = $36,589.19