A sum of money at compound interest, compounded annually, amounts to Rs 9000 after 2 years and to Rs 12960 after 4 years. Find the sum.
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → Rs 6250
Under compound interest the amount is multiplied by the same growth factor every year. The ratio of the two amounts gives the factor for 2 years.
Growth factor for 2 years \(\displaystyle =\frac{12960}{9000}=1.44\)
So the yearly factor is 1.2, a rate of 20%
Sum \(=9000\div1.2^{2}=6250\)
The sum is Rs 6250.
Why the other options are incorrect
Option (1) Rs 7500 — Incorrect. Rs 7500 grows to Rs 10800 in 2 years at 20%, not Rs 9000.
Option (2) Rs 5000 — Incorrect. Rs 5000 grows to Rs 7200 in 2 years at 20%, not Rs 9000.
Option (4) Rs 6000 — Incorrect. Rs 6000 grows to Rs 8640 in 2 years at 20%, not Rs 9000.