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The compound interest on a certain sum of money at a certain rate for 2 years is 40.80 and the simple interest on the same sum is 40 at the same rate and for the same time. The rate of interest is
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- 2% per annum
- 3% per annum
- 4% per annum
- 5% per annum
Correct Option: C
Here , Compound Interest ( CI ) = ₹ 40.80 , Simple Interest ( SI ) = ₹ 40
Let the principal be P and rate of interest be r percent per annum. Then,
| C.I. = P |  |  | 1 + |  | 2 | − 1 |  | |
| 100 |
| ⇒ 40.80 = P | | | 1 + | | 2 | − 1 | | ....(i) | |
| 100 |
| S.I. = | ⇒ 40 = | ...(ii) | ||
| 100 | 100 |
| ⇒ 1.02 = | | 1 + | + | − 1 | | |||
| 2r | 10000 | 100 |
| ⇒ 1.02 = | + 1 | |
| 200 |
| ⇒ | = 1.02 − 1 | |
| 200 |
⇒ r = 0.02 × 200
∴ r = 4% per annum.
We can find required answer with the help of given formula :
Here, C.I. = ₹ 40.80 , S.I. = ₹ 40 , R = ?
| C.I.= S.I. |  | 1 + | | |
| 200 |
| 40.80 = 40 | | 1 + | | |
| 200 |
| = 1 + | ||
| 4000 | 200 |
| = | ||
| 400 | 200 |
⇒ 408 = 400 + 2R
⇒ 2R = 8 ⇒ R = 4%
Hence , Rate = 4%
