At what rate per cent per annum will a sum of Rs. 15,625 amount to Rs. 21,952 in three years, if the interest is compounded annually?
1. 12%
2. 10%
3. 9%
4. 8%
1. 12%
2. 10%
3. 9%
4. 8%
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Correct Answer – Option 1 : 12%
Given:
Principal (P) = Rs. 15625
Time (T) = 3 years
Amount (A) = Rs. 21,952
Concept used:
Amount = P(1 + R/100)T
Calculation:
Let the rate of interest per annum be R.
21952 = 15625(1 + R/100)3
⇒ 21952/15625 = (1 + R/100)3
⇒ ∛(21952/15625) = 1 + R/100
⇒ 28/25 = 1 + R/100
⇒ 28/25 – 1 = R/100
⇒ (28 – 25)/25 = R/100
⇒ 3/25 = R/100
⇒ R = (3/25) × 100
⇒ R = 3 × 4
⇒ R = 12%
∴ The rate per cent per annum is 12%.