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प्रश्न
Rachana borrowed a certain sum at the rate of 15% per annum. If she paid at the end of two years Rs 1290 as interest compounded annually, find the sum she borrowed.
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उत्तर
Let the money borrowed by Rachana be Rs x.
Then, we have:
\[CI = P \left( 1 + \frac{R}{100} \right)^n - P\]
\[1, 290 = x\left[ \left( 1 + \frac{15}{100} \right)^2 - 1 \right]\]
\[1, 290 = x\left[ 0 . 3225 \right]\]
\[x = \frac{1, 290}{0 . 3225}\]
\[ = 4, 000\]
Thus, Rachana borrowed Rs 4, 000.
संबंधित प्रश्न
Find the compound interest at the rate of 5% per annum for 3 years on that principal which in 3 years at the rate of 5% per annum gives Rs 1200 as simple 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 |
The compound interest, calculated yearly, on a certain sum of money for the second year is Rs. 1,089 and for the third year it is Rs. 1,197.90. Calculate the rate of interest and the sum of money.
Geeta borrowed Rs. 15,000 for 18 months at a certain rate of interest compounded semi-annually. If at the end of six months it amounted to Rs. 15,600; calculate :
(i) the rate of interest per annum.
(ii) the total amount of money that Geeta must pay at the end of 18 months in order to clear the account.
Find the sum, invested at 10% compounded annually, on which the interest for the third year exceeds the interest of the first year by Rs. 252.
During every financial year, the value of a machine depreciates by 12%. Find the original cost of a machine which depreciates by Rs. 2,640 during the second financial year of its purchase.
A sum of Rs. 13,500 is invested at 16% per annum compound interest for 5years. Calculate :
(i) the interest for the first year.
(ii) the amount at the end of first year.
(iii) the interest for the second year, correct to the nearest rupee.
The compound interest on ₹ 8000 at 10% p.a for 1 year, compounded half yearly is ____________
The time taken for ₹ 4400 to become ₹ 4851 at 10%, compounded half yearly is _______
The sum which amounts to ₹ 2662 at 10% p.a in 3 years, compounded yearly is _________
