Principal

Time

Rate of Compound

When Compounded

Number of Periods to be Compounded

Total Amount

Total Interest

$300

1 Year

6%

Quarterly

To solve for the total amount and the total interest earned on a principal of $300 compounded quarterly at an annual interest rate of 6% over 1 year, we can use the compound interest formula:

\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \]

where:
- $ A $ is the amount of money accumulated after n periods, including interest.
- $ P $ is the principal amount ($300).
- $ r $ is the annual interest rate (0.06).
- $ n $ is the number of times interest is compounded per year (4 for quarterly).
- $ t $ is the time the money is invested for in years (1 year).

Let's plug in the values and calculate the total amount $ A $:

\[ A = 300 \left(1 + \frac{0.06}{4}\right)^{4 \cdot 1} \]

First, calculate the quarterly interest rate:

\[ \frac{0.06}{4} = 0.015 \]

Then, calculate the number of compounding periods in a year:

\[ 4 \cdot 1 = 4 \]

Now, apply these values to the formula:

\[ A = 300 \left(1 + 0.015\right)^4 \]

\[ A = 300 \left(1.015\right)^4 \]

Next, calculate $ (1.015)^4 $:

\[ (1.015)^4 \approx 1.06136 \]

Now, multiply by the principal:

\[ A = 300 \times 1.06136 \approx 318.41 \]

So, the total amount $ A $ after 1 year is approximately $318.41.

To find the total interest earned, subtract the principal from the total amount:

\[ \text{Total Interest} = A - P \]

\[ \text{Total Interest} = 318.41 - 300 \]

\[ \text{Total Interest} \approx 18.41 \]

Therefore:
- The total amount after 1 year is approximately $318.41.
- The total interest earned is approximately $18.41.

Would you like any details or have any questions?

Here are some related questions:
1. How would the total amount change if the interest rate was compounded monthly instead of quarterly?
2. What would be the total amount if the investment period was 2 years instead of 1 year, with the same interest rate and compounding frequency?
3. How does the frequency of compounding affect the total amount?
4. What is the effective annual rate (EAR) for this investment?
5. How can the compound interest formula be adjusted for different compounding frequencies (e.g., daily, semi-annually)?
6. What would be the total amount if the principal was $500 instead of $300, with the same interest rate and compounding frequency?
7. How does continuous compounding differ from quarterly compounding, and what would be the result using continuous compounding?
8. How does the compound interest formula change if the interest rate varies over the investment period?

Tip: When dealing with compound interest, increasing the frequency of compounding periods typically results in a higher total amount, as interest is calculated and added to the principal more frequently.

Learn how to calculate compound interest for $300 invested at an annual interest rate of 6%, compounded quarterly over 1 year. This problem involves using the compound interest formula and understanding financial mathematics concepts. Suitable for Grades 10-12 students and anyone interested in financial calculations.

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