$10,000 is invested at 2% compounded annually, what is the amount after 12 years?

To find the amount after 12 years for an investment compounded annually, we can use the compound interest formula:

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

where:
- $ A $ is the future value of the investment/loan, including interest.
- $ P $ is the principal investment amount (the initial deposit or loan amount).
- $ r $ is the annual interest rate (in decimal).
- $ n $ is the number of times that interest is compounded per year.
- $ t $ is the time the money is invested or borrowed for, in years.

Given the problem:

- $ P = 10,000 $ (initial investment)
- $ r = 0.02 $ (2% annual interest rate in decimal form)
- $ n = 1 $ (compounded annually)
- $ t = 12 $ years

Substituting these values into the compound interest formula:

\[
A = 10,000 \left(1 + \frac{0.02}{1}\right)^{1 \times 12}
\]

\[
A = 10,000 \left(1 + 0.02\right)^{12}
\]

\[
A = 10,000 \times (1.02)^{12}
\]

Now, calculate $ (1.02)^{12} $:

\[
(1.02)^{12} \approx 1.26824
\]

Therefore:

\[
A \approx 10,000 \times 1.26824
\]

\[
A \approx 12,682.40
\]

The amount after 12 years will be approximately **$12,682.40**.

---

Would you like more details, or do you have any questions? Here are some related questions for further exploration:

1. How would the future value change if the interest rate were increased to 3% compounded annually?
2. What would be the amount after 12 years if the interest were compounded semi-annually instead of annually?
3. How long would it take for the investment to double at a 2% interest rate compounded annually?
4. What would the future value be if the initial investment were $15,000 instead of $10,000 at the same interest rate and time period?
5. How does continuous compounding affect the future value compared to annual compounding?

**Tip:** When dealing with compound interest, the frequency of compounding can significantly affect the total amount of interest earned over time.

Learn how to calculate the amount after 12 years for an investment compounded annually at a 2% interest rate. Understand the compound interest formula and its application with a step-by-step solution. Suitable for high school students and anyone interested in financial mathematics.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation