Question

You would like to accumulate $2,000,000 for retirement. You have determined that you can afford to save $30,000 per year toward your retirement goal, and you will be able to earn a return of 9 percent per year on your investments.

Required:

Assuming that your annual $30,000 deposits are made at the end of each year, how long will it take for you to accumulate the $2,000,000 you desire? (Enter rounded answer as directed, but do not use rounded numbers in intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).)

Period

years

Answer 1

Future value of annuity=Annuity[(1+rate)^time period-1]/rate

2,000,000=30,000[(1.09)^time period-1]/0.09

2,000,000=333,333.33[(1.09)^time period-1]

[(1.09)^time period-1]=(2,000,000/333,333.33)

(1.09)^time period=(2,000,000/333,333.33)+1

Taking log on both sides;

time period*log 1.09=log 7

time period=log 7/log 1.09

=22.58 years(Approx).