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प्रश्न
At what rate percent per annum will a sum of Rs 4000 yield compound interest of Rs 410 in 2 years?
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उत्तर
Let the rate percent be R.
We know that:
\[CI = P \left( 1 + \frac{R}{100} \right)^n - P\]
\[410 = 4, 000 \left( 1 + \frac{R}{100} \right)^2 - 4, 000\]
\[4, 410 = 4, 000 \left( 1 + \frac{R}{100} \right)^2 \]
\[ \left( 1 + \frac{R}{100} \right)^2 = \frac{4, 410}{4, 000}\]
\[ \left( 1 + \frac{R}{100} \right)^2 = 1 . 1025\]
\[ \left( 1 + \frac{R}{100} \right)^2 = \left( 1 . 05 \right)^2 \]
\[1 + \frac{R}{100} = 1 . 05\]
\[\frac{R}{100} = 0 . 05\]
R = 5
Thus, the required rate percent is 5.
संबंधित प्रश्न
Kamala borrowed from Ratan a certain sum at a certain rate for two years simple interest. She lent this sum at the same rate to Hari for two years compound interest. At the end of two years she received Rs 210 as compound interest, but paid Rs 200 only as simple interest. Find the sum and the rate of interest.
Find the amount and the compound interest.
| No. | Principal (₹) | Rate (p.c.p.a.) | Duration (Years) |
| 1 | 2000 | 5 | 2 |
| 2 | 5000 | 8 | 3 |
| 3 | 4000 | 7.5 | 2 |
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