Question : The difference between the compound interest (compounding half-yearly) for 1 year and the simple interest for 1 year on a certain sum lent out at the annual rate of 10% is Rs, 25. What is the sum?
Option 1: Rs. 12000
Option 2: Rs. 6000
Option 3: Rs. 8000
Option 4: Rs. 10000
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Correct Answer: Rs. 10000
Solution : Given, Difference between compound interest and simple interest = Rs. 25, Annual interest rate = 10% We know, Compound Interest for 1 year = $P[(1 + \frac{r}{100})^n- 1]$, where $r$ is the annual interest rate and $n$ is the number of compounding periods. Simple Interest for 1 year = $\frac{P × r × t}{100}$, where $r$ is the annual interest rate and $t$ is the time in years. Let the principal sum be $P$. The given difference is: ⇒ $P[(1 + \frac{5}{100})^2 - 1] - \frac{P × 10 × 1}{100} = 25$ ⇒ $P[(1+0.05)^2-1]-\frac{P}{10}=25$ ⇒ $P[(1.05)^2-1]-\frac{P}{10}=25$ ⇒ $P[1.1025-1]-0.1P=25$ ⇒ $0.1025P-0.1P=25$ ⇒ $0.0025P=25$ ⇒ $P = \text{Rs.}\ 10000$ Hence, the correct answer is Rs. 10000.
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Question : What is the compound interest for 1 year on a sum of Rs. 18000 at the annual rate of 20% per annum compounding half-yearly?
Option 1: Rs. 3780
Option 2: Rs. 2450
Option 3: Rs. 4500
Option 4: Rs. 3650
Question : Rs. 6000 is lent at the rate of 20% per annum on compound interest (compounded half yearly). What will be the compound interest of 18 months?
Option 1: Rs. 1825
Option 2: Rs. 1986
Option 3: Rs. 1876
Option 4: Rs. 2036
Question : A certain sum was invested at the rate of 10% for 2 years at Compound interest and compounded annually. The same sum was invested for the same period and the same rate of interest at Simple interest. If the difference between Compound interest and Simple interest was Rs. 200 find the sum.
Option 1: Rs. 30,000
Option 2: Rs. 25,000
Option 3: Rs. 22,000
Option 4: Rs. 20,000
Question : At a certain sum of money with the interest rate of 6% per annum for 4 years, the simple interest is Rs. 4500. Find the compound interest (compounding annually) of 2 years at the same sum when the rate of interest is 4% per annum.
Option 1: Rs. 1,530
Option 2: Rs. 1,430
Option 3: Rs. 1,830
Option 4: Rs. 1,560
Question : The difference between simple interest on a certain sum at the annual rate of 8 percent for 5 years and 6 years is Rs. 26. What is the sum?
Option 1: Rs. 240
Option 2: Rs. 360
Option 3: Rs. 325
Option 4: Rs. 290
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