Compound interest formula example with solution

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compound interest formula example with solution.

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Compound Interest Formula Example with Solution

Answer:

1. Understanding the Compound Interest Formula

The compound interest formula is used to calculate the final amount (A) of an investment or loan after interest has been added multiple times over a certain period. The general formula is:

A = P \left(1 + \frac{r}{n}\right)^{n \times t}

Where:

  • A = Final amount (principal + accrued interest)
  • P = Initial principal (starting amount)
  • r = Annual interest rate (as a decimal)
  • n = Number of compounding periods per year
  • t = Total number of years

2. Step-by-Step Example

Suppose you invest $1{,}000 at an annual interest rate of 5% (i.e., r = 0.05) compounded annually (n = 1) for 3 years (t = 3).

  1. Convert rate to decimal: 5% = 0.05

  2. Plug values into the formula:

    A = 1000 \left(1 + \frac{0.05}{1}\right)^{1 \times 3}

  3. Calculate within parentheses: 1 + 0.05 = 1.05

  4. Raise to the power of 3: (1.05)^3 \approx 1.157625

  5. Multiply by the principal: 1000 \times 1.157625 \approx 1157.63

So, the final amount after 3 years is approximately $1{,}157.63. The total interest earned is $1{,}157.63 - 1{,}000 = $157.63.

3. Year-by-Year Breakdown

Year Opening Principal (USD) Interest Earned (USD) Closing Amount (USD)
1 1,000.00 1,000 × 0.05 = 50.00 1,050.00
2 1,050.00 1,050 × 0.05 = 52.50 1,102.50
3 1,102.50 1,102.50 × 0.05 = 55.13 1,157.63

Final Amount: $1{,}157.63

4. Key Takeaways

  • Compound interest grows faster than simple interest because interest is earned on both the principal and the accumulated interest.
  • The more frequent the compounding (monthly, daily, etc.), the greater the final amount.

References:

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