Question**: A bank offers a compound interest rate of 5% per annum, compounded annually. If you deposit $1000, how much will the amount be after 3 years? - AMAZONAWS

Understanding the Context

Question: A bank offers a compound interest rate of 5% per annum, compounded annually. If you deposit $1,000, how much will the amount be after 3 years?

If you’ve ever wondered how your savings grow when earning compound interest, this real-world example shows exactly how much your $1,000 deposit will grow in just 3 years at a 5% annual rate, compounded yearly.

Understanding Compound Interest

Compound interest is interest calculated on the initial principal and the accumulated interest from previous periods. Unlike simple interest, which is earned only on the original amount, compound interest enables your money to grow more rapidly over time — a powerful advantage for long-term savings and investments.

Key Insights

The Formula for Compound Interest

The formula to calculate compound interest is:

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

Where:
- \( A \) = the amount of money accumulated after n years, including interest
- \( P \) = principal amount ($1,000 in this case)
- \( r \) = annual interest rate (5% = 0.05)
- \( n \) = number of times interest is compounded per year (1, since it’s compounded annually)
- \( t \) = time the money is invested or borrowed for (3 years)

Applying the Values

Final Thoughts

Given:
- \( P = 1000 \)
- \( r = 0.05 \)
- \( n = 1 \)
- \( t = 3 \)

Plug these into the formula:

\[
A = 1000 \left(1 + \frac{0.05}{1}\right)^{1 \ imes 3}
\]
\[
A = 1000 \left(1 + 0.05\right)^3
\]
\[
A = 1000 \ imes (1.05)^3
\]

Now calculate \( (1.05)^3 \):

\[
1.05^3 = 1.157625
\]

Then: