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A certain amount of money at r%, compounded annually after two and three years becomes ₹ 1440 and ₹ 1728 respectively is
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- 5
- 10
- 15
- 20
Correct Option: D
Given in question , A1 = ₹ 1440 , T1 = 2 years
and A2 = ₹ 1728 , T2 = 3 years
If the principal be ₹ P and rate = r% , then
| A = P |  | 1 + |  | T | |
| 100 |
| ⇒ 1440 = P | | 1 + | | 2 | ..... (i) | |
| 100 |
| and 1728 = P | | 1 + | | 3 | ..... (ii) | |
| 100 |
On dividing equation (ii) by (i),
| = 1 + | ||
| 1440 | 100 |
| ∴ | = | − 1 | ||
| 100 | 1440 |
| = | = | ||
| 1440 | 1440 |
| ⇒ r = | |
| 1440 |
∴ r = 20% per annum
We can find required answer with the help of given formula :
Here, b – a = 3 – 2 = 1 and B = Rs 1728 , A = Rs. 1440
| R% = | | − 1 | | × 100% | |
| A |
| R% = | | − 1 | | × 100% | |
| 1440 |
| R% = | | | × 100% | |
| 1440 |
| R% = |  |  | × 100% = 20% | |
| 1440 |
