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At what rate per annum will ₹ 32000 yield a compound interest of ₹ 5044 in 9 months interest being compounded quarterly ?
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- 20%
- 32%
- 50%
- 80%
Correct Option: A
Here , P = ₹ 32000 , compound interest ( CI ) = ₹ 5044 , T = 9 months = ( 3 / 4 ) years
Let the rate of CI be R percent per annum.
| ∴ CI = P |  |  | 1 + |  | T | − 1 |  | |
| 100 |
| ⇒ 5044 = 32000 | | | 1 + | | 3 | − 1 | | |
| 400 |
[∵ Interest is compounded quarterly]
| ⇒ | = | | 1 + | | 3 | − 1 | ||
| 32000 | 400 |
| ⇒ | | 1 + | | 3 | − 1 = | ||
| 400 | 8000 |
| ⇒ | | 1 + | | 3 | = 1 + | ||
| 400 | 8000 |
| ⇒ | | 1 + | | 3 | = | = | | | 3 | |||
| 400 | 8000 | 20 |
| ⇒ 1 + | = | ⇒ | = | − 1 = | |||||
| 400 | 20 | 400 | 20 | 20 |
| ⇒ R = | = 20 | |
| 20 |
