The compound interest on ₹30000 at 10% per annum for n years is ₹9930. The value of n is:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 3
Compound interest is the amount minus the principal, and the amount after \(n\) years at \(r\%\) is \(P\left(1+\frac{r}{100}\right)^n\). So the amount is found first, and then the power of 1.1 that gives it.
Amount: ₹30000 + ₹9930 = ₹39930
\(30000\times(1.1)^n=39930\)
\(\displaystyle (1.1)^n=\frac{39930}{30000}=1.331\)
\(1.331=1.1\times1.1\times1.1=(1.1)^3\), so \(n=3\)
Tip: At 10% a year, the amount is multiplied by 1.1, 1.21, 1.331, 1.4641 after 1, 2, 3 and 4 years; knowing these four numbers settles such questions at a glance.