Math Problem Statement

A person invests Rs. 8500 in a securities which pays 30% interest pa compounded annually. What is the approximate value of compound inetrest earned?

Solution

To calculate the compound interest, we use the formula:

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

Where:

  • AA = the amount (final value of investment)
  • PP = the principal (initial investment)
  • rr = annual interest rate
  • tt = time (in years)

Given:

  • P=8500P = 8500
  • r=30%r = 30\%
  • t=1t = 1 year (since it's compounded annually)

Step 1: Calculate the amount AA.

A=8500×(1+30100)1=8500×1.30=11050A = 8500 \times \left(1 + \frac{30}{100}\right)^1 = 8500 \times 1.30 = 11050

Step 2: Calculate the compound interest.

Compound Interest=AP=110508500=2550\text{Compound Interest} = A - P = 11050 - 8500 = 2550

So, the approximate value of the compound interest earned is Rs. 2550.

Do you want more details or have any questions?

Here are 5 related questions for further exploration:

  1. How would the compound interest change if the time period is 2 years?
  2. What would be the value of the investment if the interest was compounded semi-annually?
  3. How does compound interest differ from simple interest?
  4. How does increasing the interest rate to 40% affect the compound interest?
  5. What would the compound interest be for a different principal, say Rs. 10,000?

Tip: For better financial returns, always check how frequently the interest is compounded. More frequent compounding leads to higher interest earnings.

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Math Problem Analysis

Mathematical Concepts

Compound Interest
Exponential Growth

Formulas

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

Theorems

Compound Interest Theorem

Suitable Grade Level

Grades 9-12