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 8000 for 1 year at 9% per annum compound half yearly. (You could use the year by year calculation using SI formula to verify)
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.
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.
The present population of a town is 28000. If it increases at the rate of 5% per annum, what will be its population after 2 years?
In how many years ₹ 700 will amount to ₹ 847 at a compound interest rate of 10 p.c.p.a.
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.
A man borrows Rs.10,000 at 10% compound interest compounded yearly. At the end of each year, he pays back 30% of the sum borrowed. How much money is left unpaid just after the second year ?
A man borrows Rs.10,000 at 10% compound interest compounded yearly. At the end of each year, he pays back 20% of the amount for that year. How much money is left unpaid just after the second year ?
Find the sum on which the difference between the simple interest and compound interest at the rate of 8% per annum compounded annually would be Rs. 64 in 2 years.
Calculate the amount and the compound interest on Rs. 10,000 in 3 years at 8% per annum.
Calculate the compound interest on Rs. 5,000 in 2 years; if the rates of interest for successive years be 10% and 12% respectively.
Calculate the compound interest for the second year on Rs. 15000 invested for 5 years at 6% per annum.
A man invests Rs. 9600 at 10% per annum compound interest for 3 years. Calculate :
(i) the interest for the first year.
(ii) the amount at the end of the first year.
(iii) the interest for the second year.
(iv) the interest for the third year. the interest for the first year.
Find the amount and the compound interest payable annually on the following :
Rs.25000 for 1`(1)/(2)` years at 10% per annum.
The simple interest on a certain sum for 3 years at 4% is Rs 600. Find the compound interest for the same sum at the same percent and in 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 simple interest and compound interest compounded annually on a certain sum is Rs.448 for 2 years at 8 percent per annum. Find the sum.
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.
The compound interest on ₹ 5000 at 12% p.a for 2 years, compounded annually is ___________
The annual rate of growth in population of a town is 10%. If its present population is 26620, then the population 3 years ago was _________
The difference between the C.I and S.I for 2 years for a principal of ₹ 5000 at the rate of interest 8% p.a is ___________
Depreciation value is calculated by the formula, `"P"(1 - "r"/100)^"n"`
The sum which amounts to ₹ 2662 at 10% p.a in 3 years, compounded yearly is _________
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 ______.
