Question

how long will it take money to double itself if invested at 5% compounded annually?

Answer 1

Here, Rate of interest is given 5% per annum to be compounded annually.

As the principal amount is not given, let us assume that P=100.

We have to find T, I.e the time taken to double the principal amount which will be 200 in this case.

The basic formula to calculate compound interest is -:

A_t= A₀(1+R)ⁿ

A_t= Amoun after a certain time 't'

A₀= Principal amount

R= Tate of interest

n= Number of compounding periods/years.

Let us put the values we have in the formula.

200=100 (1+0.05)ⁿ

=> 200 = 100 (1.05)ⁿ

Where n is in exponent place, generally log is used. The rule thus used is - log(x)ⁿ= n*log(x)

Let us continue with our calculation by introducing this log rule,

=> 200/100=1.05ⁿ

=> log(200/100)=log ((1.05)ⁿ)

=> log (200/100)= n*log (1.05)

=> n=log (200/100)/log (1.05)

=> n= log2/log (1.05)

=> n= 0.301/0.0211=14.265

Approximately considering, it will take 14 years to double the principal amount if compounded at 5% per annum.

Another way in Finance for finding investment's doubling time, I.e. Rule of 72.

Here, we can find the required time period by dividing 72 by the interest percentage per year.

In this case, 72/5=14.4

Again we got the same result I.e 14 years.