Find the amount of interest in the third year if $5000 is invested for 6 years at 8% p.a. compound interest.

To calculate the amount of interest in the third year under compound interest, we can follow these steps:

### Step 1: Calculate the amount at the end of the second year (A$_2$).
Using the compound interest formula:
\[
A_2 = P \left(1 + \frac{r}{100}\right)^2
\]
Where:
- $ P = 5000 $ (initial principal)
- $ r = 8\% $ (annual interest rate)

\[
A_2 = 5000 \left(1 + \frac{8}{100}\right)^2 = 5000 \times (1.08)^2 = 5000 \times 1.1664 = 5832
\]

### Step 2: Calculate the amount at the end of the third year (A$_3$).
\[
A_3 = P \left(1 + \frac{r}{100}\right)^3
\]

\[
A_3 = 5000 \left(1 + \frac{8}{100}\right)^3 = 5000 \times (1.08)^3 = 5000 \times 1.259712 = 6298.56
\]

### Step 3: Find the interest earned during the third year.
The interest earned during the third year is the difference between the amount at the end of the third year and the amount at the end of the second year.

\[
\text{Interest in 3rd year} = A_3 - A_2 = 6298.56 - 5832 = 466.56
\]

So, the amount of interest earned in the third year is **$466.56**.

Would you like more details on this process or have any questions?

### Related Questions:
1. How does compound interest differ from simple interest over the same period?
2. What would be the total interest earned after 6 years on the same investment?
3. How would the interest amount change if the rate was 10% instead of 8%?
4. How is compound interest calculated if it compounds more frequently than annually?
5. What would be the interest earned in the 5th year for this investment?

### Tip:
When dealing with compound interest, remember that the interest itself earns interest in subsequent periods, leading to exponential growth of the investment.

Learn how to calculate compound interest for an investment of $5000 at an annual rate of 8% over 6 years. This problem demonstrates the application of the compound interest formula step-by-step, providing detailed calculations and the amount of interest earned in the third year. Suitable for high school students studying financial mathematics.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation