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A certain sum of money amounts to ₹ 2,420 in 2 years and ₹ 2,662 in 3 years at some rate of compound interest, compounded annually. The rate of interest per annum is
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- 6%
- 8%
- 9%
- 10%
Correct Option: D
Let the rate of interest = R% per annum.
We know that ,
| A = P |  | 1 + |  | T | |
| 100 |
| ⇒ 2420 = P | | 1 + | | 2 | ..... (i) | |
| 100 |
| ⇒ 2662 = P | | 1 + | | 3 | ..... (ii) | |
| 100 |
Dividing equation (ii) by (i), we get
| 1 + | = | ||
| 100 | 2420 |
| ⇒ | = | − 1 | ||
| 100 | 2420 |
| ⇒ | = | = | = | ||||
| 100 | 2420 | 2420 | 10 |
| ⇒ R = | × 100% = 10% | |
| 10 |
We can find required answer with the help of given formula :
Here, a = 2 years , b = 3 years
b – a = 3 – 2 = 1 and B = Rs. 2,662 , A = Rs,2,420
| R% = | | − 1 | | × 100% | |
| A |
| R% = |  |  | − 1 | |  | × 100% | |
| 2420 |
| R% = | | | × 100% | |
| 2420 |
| R% = | × 100% = 10% | |
| 2420 |
