Advertisements
Advertisements
Question
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.
Advertisements
Solution
Let the sum be Rs P and the rate of interest be R %.
We know that Kamla paid Rs 200 as simple interest.
\[ \therefore 200 = \frac{PR(2)}{100}\]
PR = 10, 000 . . . (1)
Also, Kamla received Rs 210 as compound interest .
\[ \therefore 210 = P(1 + \frac{R}{100} )^2 - 1\]
\[ 210(10, 000) = P( R^2 + 200R)\]
210R = `"R"^2` + 200R [from (1)]
R = 10 % p . a .
Putting the equation in (1), we get:
P = 1, 000
Thus, the required sum is Rs 1, 000 and the rate of interest is 10 %
RELATED QUESTIONS
The interest on a sum of Rs 2000 is being compounded annually at the rate of 4% per annum. Find the period for which the compound interest is Rs 163.20.
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 certain sum amounts to Rs. 5,292 in two years and Rs. 5,556.60 in three years, interest being compounded annually. Find: the original sum.
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.
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.
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.
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 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 ___________
The time taken for ₹ 4400 to become ₹ 4851 at 10%, compounded half yearly is _______
Find the rate of compound interest at which a principal becomes 1.69 times itself in 2 years
