Math Problem Statement
There is 50% increase in an amount in 5 years at simple interest. The compound interest on ₹10,000 after 2 years at the same rate will be:
Solution
We are given the following details:
- Increase at Simple Interest: 50% increase in 5 years.
- Principal Amount for Compound Interest: ₹10,000
- Time for Compound Interest Calculation: 2 years
Step 1: Determine the Rate of Interest
At simple interest, the amount increases by 50% in 5 years. This means:
- The amount becomes 150% of the principal in 5 years.
- In simple interest, this is expressed as:
where is the principal, is the rate of interest, and is the time in years.
So, Solving for :
Thus, the rate of interest is per annum.
Step 2: Calculate Compound Interest
We now calculate the compound interest on ₹10,000 for 2 years at a rate of .
The formula for compound interest is: Where:
- is the amount after time ,
- is the principal,
- is the rate of interest,
- is the time period.
Substituting the values:
The total amount after 2 years is ₹12,100. The compound interest is the difference between the amount and the principal:
Final Answer:
The compound interest on ₹10,000 after 2 years at the same rate is ₹2,100.
Would you like any further details or have questions? Here are some related questions for deeper understanding:
- How does the formula for simple interest differ from compound interest?
- What happens if the interest is compounded quarterly instead of annually?
- How would the compound interest change if the time period were extended to 3 years?
- Can you calculate the total amount for a 10-year period using the same rate and compound interest?
- What is the difference between nominal interest rate and effective interest rate?
Tip: Always verify whether the interest rate is compounded annually, semi-annually, or quarterly to avoid miscalculations.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Simple Interest
Compound Interest
Percentage Increase
Rate of Interest
Formulas
Simple Interest: A = P + P × (R × T) / 100
Compound Interest: A = P × (1 + R/100)^T
Theorems
Interest Rate Calculation
Exponential Growth in Compound Interest
Suitable Grade Level
Grades 9-12
Related Recommendation
Compound Interest Calculation for Rs. 8000 over 2 Years at 10% Per Annum
Compound Interest Calculation on Rs 40,000 with Successive Rates of 10% and 15%
Calculate Compound Interest and Amount on Rs 2500 for 2 Years at 10% Per Annum
Calculate Compound Interest: $10,000 Investment at 3% Quarterly for 2 Years
Calculate Compound Interest for Rs. 15,000 over 3 Years