Question

Calculating Present Values. You have decided that you want to be a millionaire when you retire in 45 years. If you can earn an annual return of 11 percent, how much do you have to invest today? What if you can earn 5.5 percent?

Answer 1

We need to use the concept of time value of money to solve the question. According to the concept, the worth of money today is more compared to some time in the future because we can earn interest on money by investing.

Given that;
Future value is $1000000
Time period is 45 years
interest rate is 11%.
Future value=(Present value)*(1+Interest rate)^(Time period)
Substituting the values, we get;
1000000=(Present value)*(1+11%)^(45)
1000000=(Present value)*(109.5302415)
=>Present value=1000000/109.5302415
=9129.898613 or $9129.90 (Rounded to 2 decimal places)
So, we need to invest an amount of $9129.90

Calculation for 5.5% interest rate:
1000000=(Present value)*(1+5.5%)^(45)
1000000=(Present value)*11.12655409
=>Present value=1000000/11.12655409
=89875.08549 or $89875.09 (Rounded to 2 decimal places)
So, we need to invest an amount of $89875.09