The simple interest accrued on an amount of Rs. 84000 at the end of three years is Rs. 30240. What would be the compound interest accrued on the same amount at same rate in 2 years?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → Rs. 21369.6
Simple interest gives the rate; compound interest then adds interest on the first year’s interest in the second year.
The rate, from the simple interest:
Simple interest is the same every year, so one year’s interest is \(\displaystyle \frac{30240}{3}=10080\)
Rate per year, as a percentage of the principal: \(\displaystyle \frac{10080}{84000}\times100=12\%\)
Compound interest for 2 years at 12%:
Each year multiplies the amount by 1.12: \(84000\times(1.12)^{2}=84000\times1.2544=105369.6\)
Compound interest \(=105369.6-84000=\) Rs. 21369.6
Shortcut:
For 2 years, compound interest = twice one year’s simple interest + interest on one year’s interest
\(2\times10080+10080\times0.12=20160+1209.6=21369.6\)