Question

if you deposit $8000 into an account paying 9% annual interest compunded semi anually how long will it take for your money to double. round to the nearest hundreth

Answer 1

7.87 years

Explanation:

#First we determine the effective annual rate based on the 9% compounded semi annual;

`i_m=(1+i/m)^m-1\\\\=(1+0.09/2)^2-1\\\\=0.09203`

#We then use this effective rate in the compound interest formula to solve for n. Given that the principal doubles after 2 yrs:

`A=P(1+i)^n\\\\A=2P, i=i_m\\\\16000=8000(1.09203)^n\\\\2=1.09203^n\\\\n=(log \ 2)/(log \ 1.09203)\\\\=7.87324\approx7.87 \ yrs`

Hence, it takes 7.87 years for the principal amount to double.