A sum of money at compound interest, compounded annually, amounts to Rs 10000 after 1 year and to Rs 15625 after 3 years. Find the sum.
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → Rs 8000
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 \(\displaystyle =\frac{15625}{10000}=1.5625\)
So the yearly factor is 1.25, a rate of 25%
Sum \(=10000\div1.25=8000\)
The sum is Rs 8000.
Why the other options are incorrect
Option (1) Rs 7500 — Incorrect. Rs 7500 grows to Rs 9375 in 1 year at 25%, not Rs 10000.
Option (3) Rs 6400 — Incorrect. Rs 6400 grows to Rs 8000 in 1 year at 25%, not Rs 10000.
Option (4) Rs 9000 — Incorrect. Rs 9000 grows to Rs 11250 in 1 year at 25%, not Rs 10000.