Question

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

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 
$F=\frac{A((1+i)^n-1)}{i}$   where n=number of years
=>
$20000=\frac{1000((1+.07)^n-1)}{.07}$
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