In how many years will a sum of Rs. 800 become Rs. 926.10 at 10% per annum compounded semi-annually?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \(1\frac{1}{2}\)
When interest is compounded half-yearly, the rate for each period is half the yearly rate and the number of periods is twice the number of years: \(A=P\left(1+\frac{R}{200}\right)^{n}\), with \(n\) half-years. The number of periods is found by comparing the growth factor with powers of 1.05.
Rate per half-year \(=\frac{10}{2}=5\%\), so each period multiplies the sum by 1.05
Amount after \(n\) half-years: \(800\times(1.05)^{n}=926.10\)
Growth factor needed: \((1.05)^{n}=\displaystyle\frac{926.10}{800}=1.157625\)
Powers of 1.05 are 1.05, 1.1025, 1.157625, so \(n=3\) half-years
Three half-years make \(1\frac{1}{2}\) years