Question : If the amount is $3\frac{3}{8}$ times the sum after 3 years at compound interest compounded annually, then the Rate of interest per annum is:
Option 1: $25$%
Option 2: $50$%
Option 3: $16\frac{2}{3}$%
Option 4: $33\frac{1}{3}$
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Correct Answer: $50$%
Solution : Let the principal be Rs. $x$. Rate of interest = R% Time = 3 years Amount = $3\frac{3}{8}=3.375x$ We know, $\text{Total amount}=\text{Principal}×(1+\frac{\text{Rate}}{100})^{\text{Time}}$ $⇒3.375x = x(1 + \frac{R}{100})^{3}$ $⇒3.375 =(1 + \frac{R}{100})^{3}$ $⇒(1 + \frac{R}{100})^{3} = (1.5)^{3}$ $⇒(1 + \frac{R}{100}) = (1.5)$ $⇒\frac{R}{100}=0.5$ $\therefore R=50$% Hence, the correct answer is $50$%.
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Question : At what rate of compound interest (compounding annually) per annum will a sum of Rs. 1,000 become Rs. 1,060.90 in 2 years?
Option 1: 2% per annum
Option 2: 4% per annum
Option 3: 3% per annum
Option 4: 5% per annum
Question : The simple interest on a certain sum of money at the rate of 5% per annum for 8 years is Rs. 840. The rate of interest for which the same amount of interest can be received on the same sum after 5 years is:
Option 1: 7% per annum
Option 2: 8% per annum
Option 3: 9% per annum
Option 4: 10% per annum
Question : The simple interest on a sum of money is $\frac {1}{16}$th of the principal and the number of years is equal to the rate per cent per annum. The rate per annum is:
Option 1: $1\frac{1}{2}$%
Option 2: $2\frac{1}{2}$%
Option 3: $3\frac{1}{2}$%
Option 4: $4\frac{1}{2}$%
Question : If INR 2,000 is invested at a simple interest rate of 5% per annum and the interest is added to the principal after 10 years, then in how many years will it amount to INR 4,000 at the same rate of interest?
Option 1: $18 \frac{2}{3}$ years
Option 2: $16 \frac{1}{3}$ years
Option 3: $16 \frac{2}{3}$ years
Option 4: $18 \frac{1}{3}$ years
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
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