A sum triples in ten years under compound interest at a certain rate of interest, the interest is being compounded annually. In how many years, it would become nine times ?
20 years
30 years
40 years
50 years
Answer is Wrong!
Answer is Right!
This question was previously asked in
UPSC CAPF – 2020
We are given that the sum triples in ten years:
$3P = P(1+r)^{10} \implies (1+r)^{10} = 3$.
We want to find the number of years ‘t’ it takes for the sum to become nine times the principal:
$9P = P(1+r)^t \implies (1+r)^t = 9$.
Since $9 = 3^2$, we can substitute the value of 3 from the first equation:
$(1+r)^t = ( (1+r)^{10} )^2$
$(1+r)^t = (1+r)^{10 \times 2}$
$(1+r)^t = (1+r)^{20}$
Equating the exponents, we get $t = 20$.
It would take 20 years for the sum to become nine times.