Question : On a certain sum, the interest is compounded annually. If the compound interest for the second year is INR 400 and the compound interest for the fourth year is 576, then what is the rate of interest per annum?
Option 1: 20%
Option 2: 25%
Option 3: 15%
Option 4: 44%
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Correct Answer: 20%
Solution : When compounded annually, $ A= P(1+\frac{R}{100})^{T}$, Where $A$ is the total amount, $P$ is the principal amount, $R$ is the rate of interest per annum, and $T$ is the time in years. According to the question, $P(1+\frac{R}{100})^2-P(1+\frac{R}{100})=400$ -----------------(1) $P(1+\frac{R}{100})^4-P(1+\frac{R}{100})^3=576$ -----------------(2) From equation (1) we get, $P(1+\frac{R}{100})[(1+\frac{R}{100})-1]=400$ ---------------(3) From equation (2) we get, $P(1+\frac{R}{100})^3[(1+\frac{R}{100})-1]=576$ ---------------(4) Dividing equation (4) by equation (3), $(1+\frac{R}{100})^2=\frac{576}{400}$ ⇒ $(1+\frac{R}{100})^2=(\frac{24}{20})^2$ ⇒ $(1+\frac{R}{100})=(\frac{24}{20})$ ⇒ $\frac{R}{100}=\frac{24}{20}-1$ ⇒ $R=20$% Hence, the correct answer is 20%.
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Question : The difference between the compound interest and the simple interest on an amount of INR 1,500 for 2 years, at a given rate of interest per annum, is INR 60. What is the rate of interest per annum, if in the case of compound interest, the interest is compounded annually?
Option 2: 15%
Option 3: 25%
Option 4: 12.5%
Question : The compound interest received on INR 18,000 for 2 years is INR 7,920 when the interest is compounded annually. What is the rate of interest per annum?
Option 1: 15%
Option 2: 12.5%
Option 3: 20%
Option 4: 25%
Question : On a certain sum of money, the simple interest for 2 years is INR 150 at the rate of 10% per annum. What is the difference between compound interest and simple interest for 2 years if, in the case of compound interest, interest is compounded annually at the rate of 10% per annum?
Option 1: INR 5
Option 2: INR 10
Option 3: INR 7.5
Option 4: INR 12.5
Question : The simple interest on a certain sum of money for 2 years at 7% per annum is double the compound interest on INR 1,000 for 2 years at 10% per annum, compounded annually. What is the sum placed on simple interest?
Option 1: INR 1,000
Option 2: INR 2,000
Option 3: INR 3,000
Option 4: INR 4,000
Question : The difference between the simple interest and the compound interest at the same rate for INR 32,000 for 2 years is 80. What is the rate of interest, if in the case of compound interest, interest is compounded annually?
Option 1: 8% per annum
Option 2: 2% per annum
Option 3: 5% per annum
Option 4: 12% per annum
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