Question

$1000 is invested at 8% per annum compounded quarterly. Calculate the interest earned after 6 years

Answer 1

To calculate the interest earned on an investment compounded quarterly, we can use the formula for compound interest:

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

where:
- \( A \) is the amount of money accumulated after n years, including interest.
- \( P \) is the principal amount (the initial amount of money).
- \( r \) is the annual interest rate (decimal).
- \( n \) is the number of times that interest is compounded per year.
- \( t \) is the number of years the money is invested or borrowed.

In this case:
- \( P = 1000 \)
- \( r = 0.08 \) (8% expressed as a decimal)
- \( n = 4 \) (since interest is compounded quarterly)
- \( t = 6 \)

Plugging these values into the formula:

\[
A = 1000 \left(1 + \frac{0.08}{4}\right)^{4 \times 6}
\]

Calculating the values inside the brackets:

\[
\frac{0.08}{4} = 0.02
\]

So, we have:

\[
A = 1000 \left(1 + 0.02\right)^{24}
\]
\[
A = 1000 \left(1.02\right)^{24}
\]

Now calculating \( (1.02)^{24} \):

\[
(1.02)^{24} \approx 1.6084 \quad \text{(using a calculator for the exponent)}
\]

Now substituting back into the formula for \( A \):

\[
A \approx 1000 \times 1.6084 \approx 1608.40
\]

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

\[
\text{Interest} = A - P = 1608.40 - 1000 = 608.40
\]

Thus, the interest earned after 6 years is approximately **$608.40**.