In how much time will a sum of ₹64,000 amount to ₹68,921 at 5% per annum, interest being compounded half yearly ?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(1\frac{1}{2}\) years
With interest compounded half-yearly, the rate for each half-year is half the yearly rate, and each half-year is one conversion period.
Rate per half-year: \(2.5\%\), so the amount grows by the factor \(\displaystyle1+\frac{2.5}{100}=\frac{41}{40}\) each half-year
\(\displaystyle\frac{68921}{64000}=\left(\frac{41}{40}\right)^3\), since \(41^3=68921\) and \(40^3=64000\)
So there are 3 half-years, that is, \(1\frac{1}{2}\) years
Tip: When an amount and a principal are perfect cubes (or squares) like 68,921 and 64,000, take the cube root of each: the ratio 41 : 40 shows the growth factor at once.