Question

How many years does it take for an annuity of $ 1,000 to grow to $ 20,000, assuming k = 7%?

a. 12.94
b. 13.02
c. 14.18
d. 15.67
e. none of the above?

Answer 1

For an annual deposit of A=$1000 (at the end of the year) at an annual interest rate of i=7% compounded yearly, the future value

`F=(A((1+i)^n-1))/(i)` where n=number of years
=>

`20000=(1000((1+.07)^n-1))/(.07)`
on simplification

`1.4=(1.07)^n-1`

`(1.07)^n=2.4`
take logs and solve for n

`n=log(2.4)/log(1.07)`

`n=12.939` years, to the nearest 0.001 year