Question

How do you calculate compount interest?

Answer 1

Compound interest can be calculated using the formula:

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

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.

To calculate the compound interest earned, you can subtract the principal from the total amount:

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

### Steps to Calculate Compound Interest:
1. Determine the principal amount (\( P \)).
2. Specify the annual interest rate (\( r \)) and convert it to decimal form (e.g., 5% becomes 0.05).
3. Decide how frequently the interest is compounded (e.g., annually, semi-annually, quarterly, monthly).
4. Determine the time the money is invested or borrowed (\( t \)) in years.
5. Plug the values into the formula to calculate \( A \).
6. Subtract the principal (\( P \)) from \( A \) to find the compound interest.

### Example:
Suppose you invest $1,000 (principal) at an annual interest rate of 5% (0.05) for 10 years, compounded annually (\( n = 1 \)).

1. \( P = 1000 \)
2. \( r = 0.05 \)
3. \( n = 1 \)
4. \( t = 10 \)

Plugging these values into the formula:

\[
A = 1000 \times (1 + 0.05/1)^{1 \times 10} = 1000 \times (1 + 0.05)^{10} = 1000 \times (1.05)^{10}
\]

Calculating \( (1.05)^{10} \):

\[
(1.05)^{10} \approx 1.62889
\]

Now, calculate \( A \):

\[
A \approx 1000 \times 1.62889 \approx 1628.89
\]

Finally, to find the compound interest:

\[
\text{Compound Interest} = A - P = 1628.89 - 1000 \approx 628.89
\]

So, the compound interest earned over 10 years would be approximately $628.89.