Calculate the amount of interest earned if R6674 is invested at the end of every 3 months for a period of 5years and interest is calculated at 5.6% per annum compounded quarterly

To calculate the total interest earned on an investment of R6674 made at the end of every 3 months for 5 years, with interest compounded quarterly at 5.6% per annum, we will use the **future value of an ordinary annuity** formula.

The formula is:

\[
FV = P \times \frac{(1 + i)^n - 1}{i}
\]

Where:
- \(FV\) is the future value of the investment (including both principal and interest),
- \(P\) is the amount of each payment (R6674),
- \(i\) is the interest rate per period (quarterly rate),
- \(n\) is the total number of payments (periods).

### Step 1: Identify the variables
- **Annual interest rate**: 5.6% = 0.056
- **Quarterly interest rate**: \( i = \frac{0.056}{4} = 0.014 \)
- **Number of periods**: Since payments are made quarterly over 5 years, \( n = 5 \times 4 = 20 \) periods.

### Step 2: Substitute into the formula
\[
FV = 6674 \times \frac{(1 + 0.014)^{20} - 1}{0.014}
\]

Let me compute this.The future value of the investment, including both principal and interest, is approximately R152,816.93.

### Step 3: Calculate the total interest earned
To find the total interest earned, we subtract the total principal invested from the future value:

\[
\text{Total principal} = 6674 \times 20 = 133,480
\]
\[
\text{Interest earned} = 152,816.93 - 133,480 = 19,336.93
\]

Thus, the total interest earned is approximately **R19,336.93**.

Would you like further details or have any questions?

Here are some related questions:
1. How would the interest change if the investment period was 10 years?
2. What is the effect of increasing the annual interest rate to 6%?
3. How is the formula different for continuous compounding?
4. What if payments were made at the beginning of each period instead of the end?
5. How does compounding frequency (e.g., monthly vs. quarterly) impact the final amount?

**Tip:** Regularly increasing the compounding frequency (e.g., quarterly to monthly) increases the future value due to more frequent application of interest.

Calculate the amount of interest earned if R6674 is invested at the end of every 3 months for a period of 5 years and interest is calculated at 5.6% per annum compounded quarterly.

Discover how to calculate the interest earned on an investment of R6674 made every 3 months over 5 years with an interest rate of 5.6% compounded quarterly. This step-by-step solution covers key financial concepts such as annuities, compound interest, and the future value formula. Suitable for Grades 10-12.

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