Advertisements
Advertisements
प्रश्न
Ashok borrowed Rs. 12,000 at some rate on compound interest. After a year, he paid back Rs.4,000. If the compound interest for the second year is Rs. 920, find:
- The rate of interest charged
- The amount of debt at the end of the second year
Advertisements
उत्तर
(i) Let X% be the rate of interest charged.
For 1st year :
P = Rs.12,000, R = X% and T = 1
⇒ Interest (I) = `[12,000 xx "X" xx 1]/[100]` = 120X
For 2nd year:
After a year, Ashok paid back Rs. 4,000.
P = Rs.12,000 + Rs. 120X - Rs. 4,000 = Rs. 8,000 + Rs.120X
⇒ Interest (I) = `[( 8000 + 120"X") xx 1]/[100]` = ( 80X + 1.20X2 )
The compound interest for the second year is Rs. 920.
Rs. ( 80X + 1.20X2 ) = Rs. 920
⇒ 1.20X2 + 80X - 920 = 0
⇒ 3X2 + 200X - 2300 = 0
⇒ 3X2 + 230X - 30X - 2300 = 0
⇒ X(3X + 230) -10(3X + 230) = 0
⇒ (3X + 230)(X - 10) = 0
⇒ X = -230/3 or X = 10
As rate of interest cannot be negative so x = 10.
Therefore the rate of interest charged is 10%.
(ii) For 1st year :
Interest = Rs.120X = Rs.1200
For 2nd year :
Interest = Rs.( 80X + 1.20X2 ) = Rs.920
The amount of debt at the end of the second year is equal to the addition of principal of the second year and interest for the two years.
Debt = Rs. 8,000 + Rs. 1200 + Rs. 920 = Rs. 10,120
APPEARS IN
संबंधित प्रश्न
Calculate the amount and compound interest on Rs 10000 for 1 year at 8% per annum compounded half yearly.
Find the difference between the compound interest and simple interest. On a sum of Rs 50,000 at 10% per annum for 2 years.
What will Rs 125000 amount to at the rate of 6%, if the interest is calculated after every 3 months?
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.
The difference between the compound interest and simple interest on a certain sum for 2 years at 7.5% per annum is Rs 360. Find the sum.
The difference in simple interest and compound interest on a certain sum of money at \[6\frac{2}{3} %\] per annum for 3 years is Rs 46. Determine the sum.
At what rate percent per annum will a sum of Rs 4000 yield compound interest of Rs 410 in 2 years?
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 |
A sum is invested at compound interest, compounded yearly. If the interest for two successive years is Rs. 5,700 and Rs. 7,410. calculate the rate of interest.
Mohit invests Rs. 8,000 for 3 years at a certain rate of interest, compounded annually. At the end of one year it amounts to Rs. 9,440. Calculate:
- the rate of interest per annum.
- the amount at the end of the second year.
- the interest accrued in the third year.
The value of a machine depreciated by 10% per year during the first two years and 15% per year during the third year. Express the total depreciation of the machine, as percent, during the three years.
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.
Saurabh invests Rs. 48,000 for 7 years at 10% per annum compound interest. Calculate:
(i) the interest for the first year.
(ii) the amount at the end of second year.
(iii) the interest for the third year.
A sum of Rs. 8,000 is invested for 2 years at 10% per annum compound interest. Calculate:
(i) interest for the first year.
(ii) principal for the second year.
(iii) interest for the second year.
(iv) the final amount at the end of the second year
(v) compound interest earned in 2 years.
Rekha borrowed Rs. 40,000 for 3 years at 10% per annum compound interest. Calculate the interest paid by her for the second year.
Peter borrows ₹ 12,000 for 2 years at 10% p.a. compound interest. He repays ₹ 8,000 at the end of the first year. Find:
- the amount at the end of the first year, before making the repayment.
- the amount at the end of the first year, after making the repayment.
- the principal for the second year.
- the amount to be paid at the end of the second year, to clear the account.
The simple interest on a certain sum of money at 4% p.a. for 2 years is Rs1500. What will be the compound interest on the same sum for the same time?
The compound interest payable annually on a certain sum for 2 years is Rs 40.80 and the simple interest is Rs 40. Find the sum and the rate percent.
The difference between C.I. payable annually and S.I. on Rs.50,000 for two years is Rs.125 at the same rate of interest per annum. Find the rate of interest.
A principal becomes ₹ 2028 in 2 years at 4% p.a compound interest. Find the principal
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 _________
Suppose for the principal P, rate R% and time T, the simple interest is S and compound interest is C. Consider the possibilities.
- C > S
- C = S
- C < S
Then
Suppose a certain sum doubles in 2 years at r % rate of simple interest per annum or at R% rate of interest per annum compounded annually. We have ______.
The compound interest on Rs 50,000 at 4% per annum for 2 years compounded annually is ______.
Compound interest is the interest calculated on the previous year’s amount.
