Compound Interest

[sampath]

A total of $1000 was invested at compounded annual interest rate. At the end of 12 years, the total value will be $4000. How many years are needed to reach a total of $8,000?

OA given is 18

[Anurag@Gurome]

A total of $1000 was invested at compounded annual interest rate. At the end of 12 years, the total value will be $4000. How many years are needed to reach a total of $8,000?

Say, the rate of interest is r percent per year and after n years the investment will reach a total of $8000.

Hence, after 12 years $1000 will become $1000*(1 + r/100)^12
And, after n years $1000 will become $1000*(1 + r/100)^n

Now, 1000*(1 + r/100)^12 = 4000 ---> (1 + r/100)^(12n) = 4^n ........... (1)
And, 1000*(1 + r/100)^n = 8000 ---> (1 + r/100)^(12n) = 8^12 .......... (2)

Dividing (1) by (2) we have, 1 = 4^n/8^12
Therefore, 4^n = 8^12
--> 2^2n = 2^36
--> 2n = 36
--> n = 18