Question

You win the grand prize on a game show. You have the following choices:

Option 1: $1-million dollars paid as a $25 000 annuity every year over 40 years.

Option 2: The present value of option 1 if the current interest rate is 4%, compounded annually.

Determine the present value of option 2.

If you can reinvest the $1 000 000 at 5%, compounded annually, over 40 years how much more money would you have than if you accepted Option 1?

Answer 1

If we are receiving the annuity of $25000, then for calculating the present value of option1, we will use the present value of annuity table.

Present value of option 2 = $25000 * PVIFA (4%, 40 years)

Now, we will find out value of PVIFA (4%, 40 years) from the present value of annuity table at 4% for 40 years.

The value of PVIFA(4%,40 years) arrived is 19.79. Now, putting this value in the equation above, we get,

Present value of option 2 = $25000 * 19.79

Present value of option 2 = $494750

If we reinvest $1000000 at 5% compounded annually over 40 years, then for calculating the amount, we will use the following formula:

FV = PV * (1+R%)ⁿ

where, FV= Future value, PV= Present value = $1000000, R= Rate of interest = 5% and n= time period = 40

Now, putting these values in the above equation, we get,

FV=$1000000 * (1+ 5%)⁴⁰

FV = $1000000 * (1.05)⁴⁰

FV = $1000000 * 7.039988

FV = $7039988.71212

In option 1 we will get $1000000, while here we are getting $7039988.7212,

so we will get $6039988.7212 (i.e. $7039988.7212 - $1000000) more money.