Question

12. Larry received an inheritance of $25,000 he plans to invest in an account that pays interest compounded monthly. What interest rate must the money earn to have $1,000,000 in the bank in bank when he retires in 40 years?

Answer 1

Let the interest rate per annum compounded monthly by X%

Give present value of investement = 25000

Future value of investment =1000000

Also, Future Value = Present value*(1+Interest rate/ n)^time*n

where n is the number of compounding in a year

1000000=25000*(1+X%/12)^(40*12)

1000000/25000=(1+X%/12)^480

40= (1+X%/12)^480

40^(1/480)= 1+X%/12

1.007715=1+ X%/12

0.007715=X%/12

0.7715%*12= X

X= 9.2577%

Hence the interest rate has to be 9.2577% per annum compunded monthly in order to have 1,000,000 at the end of year 40