Math Problem Statement

Find the amount and the compound interest on Rs 2500 for 2 years at 10% per annum, compounded annually.

03:08 View Solution

Solution

To find the compound interest and the amount, we can use the following formula:

A=P(1+r100)nA = P \left(1 + \frac{r}{100}\right)^n

Where:

  • AA is the amount,
  • PP is the principal (initial investment),
  • rr is the rate of interest per annum,
  • nn is the number of years.

Given:

  • P=2500P = 2500 Rs,
  • r=10%r = 10\%,
  • n=2n = 2 years.

Step 1: Calculate the Amount

A=2500(1+10100)2A = 2500 \left(1 + \frac{10}{100}\right)^2 A=2500(1+0.10)2A = 2500 \left(1 + 0.10\right)^2 A=2500×(1.1)2A = 2500 \times (1.1)^2 A=2500×1.21=3025A = 2500 \times 1.21 = 3025

So, the amount after 2 years is Rs 3025.

Step 2: Calculate the Compound Interest

Compound Interest (CI) is given by:

CI=APCI = A - P CI=30252500=525CI = 3025 - 2500 = 525

Thus, the compound interest is Rs 525.

Final Answer:

  • Amount = Rs 3025
  • Compound Interest = Rs 525

Would you like more details on any of the steps or formulas used?

Here are 5 related questions for further exploration:

  1. How would the compound interest change if the rate was 12% instead of 10%?
  2. What would the compound interest be if compounded semi-annually instead of annually?
  3. How does simple interest compare to compound interest for the same problem?
  4. What is the formula for compound interest if compounded monthly?
  5. How does the time period affect the amount of compound interest?

Tip: When working with compound interest, it's important to note whether it's compounded annually, semi-annually, or monthly, as this affects the calculations.

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Math Problem Analysis

Mathematical Concepts

Compound Interest
Exponential Growth

Formulas

A = P(1 + r/100)^n
CI = A - P

Theorems

Compound Interest Theorem

Suitable Grade Level

Grades 8-10