Understanding Interest Calculation: Simple vs. Compound
This question asks us to find the difference between the compound interest (CI) and simple interest (SI) earned on a principal amount of ₹10,000 over a period of 3 years, with an annual interest rate of 5%. Let's break down the calculation for both types of interest.
Simple Interest Calculation
Simple interest is calculated only on the initial principal amount. The formula for simple interest is:
\( SI = \frac{P \times R \times T}{100} \)Where:
- P is the Principal amount (₹10,000)
- R is the Rate of interest per year (5%)
- T is the Time period in years (3 years)
Plugging the values into the formula:
\( SI = \frac{10000 \times 5 \times 3}{100} \) \( SI = \frac{150000}{100} \) \( SI = 1500 \)So, the Simple Interest earned after 3 years is ₹1,500.
Compound Interest Calculation
Compound interest is calculated on the principal amount as well as on the accumulated interest from previous periods. The formula to calculate the total amount (A) including compound interest is:
\( A = P \left(1 + \frac{R}{100}\right)^T \)Where:
- P = ₹10,000
- R = 5%
- T = 3 years
First, let's calculate the total amount:
\( A = 10000 \left(1 + \frac{5}{100}\right)^3 \) \( A = 10000 \left(1 + 0.05\right)^3 \) \( A = 10000 \left(1.05\right)^3 \)Calculating \((1.05)^3\):
\( (1.05)^3 = 1.157625 \)Now, substitute this back into the amount formula:
\( A = 10000 \times 1.157625 \) \( A = 11576.25 \)The total amount after 3 years is ₹11,576.25. To find the Compound Interest (CI), we subtract the principal amount from the total amount:
\( CI = A - P \) \( CI = 11576.25 - 10000 \) \( CI = 1576.25 \)So, the Compound Interest earned after 3 years is ₹1,576.25.
Difference Between Compound and Simple Interest
The question asks for the difference between the compound interest and the simple interest.
Difference = CI - SI
\( \text{Difference} = 1576.25 - 1500 \) \( \text{Difference} = 76.25 \)Therefore, the difference between the compound interest and simple interest received after 3 years is ₹76.25.
Similar Questions
- Let \(x\) be the compound interest at the end of 3 years on a sum of ₹ 1000 at the rate of 10% compounded annually and \(y\) be the simple interest at the end of 3 years on a sum of ₹ 1000 at the annual rate of 11%. What is the difference between \(x\) and \(y\)?
Important Questions from Simple and Compound Both
X took a loan of Rs.1400 with simple interest for as many years as the rate of interest. If he paid Rs.1210 as interest at the end of that period, what was the rate of interest?
The S.I. on a certain sum of money for 4 years at 4 percent per annum exceeds the C.I. on the same sum for 3 years at 5 percent per annum by Rs. 57. Find the approximate sum.
Compound interest on a certain sum of money for 2 years at a rate of 'r' per cent per annum (compounding annually) is Rs. 8385. Simple interest on the same sum at the same rate for 2 years is Rs 7800. What is the value of r?
Find the difference between compound interest and simple interest on a sum of Rs. 5000 at 10% per annum for 3 years.
The difference between the compound interest and simple interest on a certain sum of money in 3 years at 5% p.a. is Rs. 6,100. What is the initial amount?
