Math Problem Statement

Solve correctly only

Find the amount at the end of 2 years on ₹1000 at 4% per annum, compounded annually.

Solution

The question asks to find the amount at the end of 2 years on ₹1000 at 4% per annum, compounded annually.

We can use the compound interest formula for this calculation:

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

Where:

  • AA is the amount after tt years,
  • PP is the principal (initial amount),
  • rr is the annual interest rate,
  • tt is the time in years.

Given:

  • P=1000P = 1000 (₹),
  • r=4%r = 4\%,
  • t=2t = 2 years.

Substitute these values into the formula:

A=1000(1+4100)2A = 1000 \left( 1 + \frac{4}{100} \right)^2 A=1000(1+0.04)2A = 1000 \left( 1 + 0.04 \right)^2 A=1000×(1.04)2A = 1000 \times (1.04)^2 A=1000×1.0816A = 1000 \times 1.0816 A=1081.60A = 1081.60

Thus, the amount after 2 years will be ₹1081.60.

Would you like further clarification or details on any part of this solution?

Relative Questions:

  1. How is compound interest different from simple interest?
  2. What happens if the interest is compounded more frequently than annually?
  3. How would the result change if the interest rate was higher or lower?
  4. What formula would be used if interest were compounded semi-annually instead of annually?
  5. Can this formula be used for non-annual compounding periods?

Tip:

Always make sure to adjust the interest rate and time period when the compounding is done more frequently than annually.

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Math Problem Analysis

Mathematical Concepts

Compound Interest
Exponential Growth

Formulas

Compound Interest Formula: A = P(1 + r/100)^t

Theorems

Interest Theorem

Suitable Grade Level

Grades 7-10