Math Problem Statement

Find the amount compounded annually on ₹25,000 for 2 years at the rate of interest of 10% and 12%, respectively.

Solution

The image contains questions involving compound interest calculations. Here's an interpretation and solution for one of the questions visible in the image.

Question Interpretation:

Find the amount compounded annually on ₹25,000 for 2 years at the rate of interest of 10% and 12%.

Formula for Compound Interest:

The formula to calculate the compound amount is: A=P×(1+r100)nA = P \times \left(1 + \frac{r}{100}\right)^n Where:

  • AA is the amount,
  • PP is the principal amount,
  • rr is the rate of interest per annum,
  • nn is the time in years.

Solution for ₹25,000 compounded annually at 10% for 2 years:

  1. P=25000P = 25000, r=10%r = 10\%, n=2n = 2: A=25000×(1+10100)2A = 25000 \times \left(1 + \frac{10}{100}\right)^2 A=25000×(1.1)2A = 25000 \times (1.1)^2 A=25000×1.21=30250A = 25000 \times 1.21 = 30250

Solution for ₹25,000 compounded annually at 12% for 2 years:

  1. P=25000P = 25000, r=12%r = 12\%, n=2n = 2: A=25000×(1+12100)2A = 25000 \times \left(1 + \frac{12}{100}\right)^2 A=25000×(1.12)2A = 25000 \times (1.12)^2 A=25000×1.2544=31360A = 25000 \times 1.2544 = 31360

Final Answers:

  • At 10% for 2 years: ₹30,250
  • At 12% for 2 years: ₹31,360

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Follow-Up Questions:

  1. What is the formula for quarterly compounding instead of annual?
  2. How would the results change if the interest rate applied was different in each year?
  3. Can you calculate the interest amount earned instead of the total amount?
  4. What happens if the time is given in months rather than years?
  5. How does compounding frequency (e.g., monthly, daily) impact the total amount?

Tip:

Always double-check the compounding frequency mentioned in a problem as it affects the formula and calculations significantly!

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Math Problem Analysis

Mathematical Concepts

Compound Interest
Exponents
Percentage

Formulas

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

Theorems

Compound Interest Theorem

Suitable Grade Level

Grades 8-10