Question
There is 60% increase in an amount in 4 years at simple interest. What will be the compound interest on Rs.49500 after 2 years at the same rate of interest? (In Rs.)
The correct answer is
15963.75
Determine the Simple Interest Rate
The problem states a 60% increase in an amount over 4 years at simple interest. We need to find the annual rate of interest (R).
- Let the Principal be P.
- Simple Interest (SI) = 60% of P = $0.60 \times P$
- Time (T) = 4 years
- Using the formula $SI = \frac{P \times R \times T}{100}$:
- $0.60 \times P = \frac{P \times R \times 4}{100}$
- Divide both sides by P (assuming P is not zero):
- $0.60 = \frac{R \times 4}{100}$
- Solve for R:
- $R = \frac{0.60 \times 100}{4}$
- $R = \frac{60}{4}$
- $R = 15\%$ per annum
Calculate Compound Interest
Now, we calculate the compound interest (CI) on Rs. 49500 for 2 years at the calculated rate of 15%.
- Principal (P) = Rs. 49500
- Rate (R) = 15% per annum
- Time (T) = 2 years
- First, calculate the Amount (A) using the compound interest formula: $A = P \left(1 + \frac{R}{100}\right)^T$
- $A = 49500 \left(1 + \frac{15}{100}\right)^2$
- $A = 49500 \left(1 + 0.15\right)^2$
- $A = 49500 (1.15)^2$
- $A = 49500 \times 1.3225$
- $A = 65463.75$
- The Compound Interest (CI) is the Amount minus the Principal: $CI = A - P$
- $CI = 65463.75 - 49500$
- $CI = 15963.75$
Therefore, the compound interest is Rs. 15963.75.
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Important Questions from Simple and Compound Both
- The difference between the interest earned on the same amount invested under compound interest and simple interest at same rate of interest for 2 years is Rs.470. If the rate of interest is 10% p.a. then find the amount invested? (In Rs.)
- Suresh lent a sum of money on compound interest in such a way that it amounted to three times in 4 years. For how much time should he invest his money so that he gets back an amount which is 9 times of the sum of money lent by him?
The compound interest on a certain sum for 3 years at 8% per annum is Rs. 1,94,784. What is the simple interest on the $\frac{9}{10}$ part of the sum for the same time but at a rate of interest per annum which is $1\frac{1}{2}$ time the rate of interest per annum as applicable for compound interest?
- The difference between the interest earned on the same amount invested under compound interest and simple interest at same rate of interest for 2 years is Rs.205. If the rate of interest is 5% p.a. then find the amount invested? (In Rs.)
- The difference between the interest earned on the same amount invested under compound interest and simple interest at same rate of interest for 2 years is Rs.945. If the rate of interest is 15% p.a. then find the amount invested? (In Rs.)
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