Time is 12 years, principle $15,000, rate 3 1/2%, compounded annually. What’s the amount and interest?

We can use the formula for compound interest to calculate both the amount and the interest. The formula is:

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

Where:
- $A$ = the future value (amount),
- $P$ = the principal (initial investment),
- $r$ = the annual interest rate (decimal form),
- $n$ = the number of times the interest is compounded per year,
- $t$ = the time the money is invested for (in years).

Given:
- $P = 15,000$,
- $r = 3.5\% = 0.035$,
- $n = 1$ (since the interest is compounded annually),
- $t = 12$ years.

Now let's compute the future value $A$:

\[
A = 15,000 \left(1 + \frac{0.035}{1}\right)^{1 \times 12}
\]

\[
A = 15,000 \left(1 + 0.035\right)^{12}
\]

\[
A = 15,000 \times (1.035)^{12}
\]

Calculating $1.035^{12}$:

\[
A = 15,000 \times 1.5114
\]

\[
A \approx 22,671
\]

So the amount after 12 years is approximately **$22,671**.

### Interest:
The interest earned is simply the total amount minus the principal:

\[
\text{Interest} = A - P = 22,671 - 15,000 = 7,671
\]

Thus, the interest earned is **$7,671**.

---

Would you like more details or have any questions? 

Here are 5 related questions for practice:

1. What would the amount be if the interest were compounded semi-annually?
2. How would the amount change if the rate were 4% instead of 3.5%?
3. If the principal were increased to $20,000, what would be the new interest?
4. How does the amount change if the time is reduced to 10 years instead of 12 years?
5. What is the difference in amount if the interest is compounded monthly instead of annually?

**Tip:** Always ensure you convert percentage rates to decimal form (e.g., 3.5% becomes 0.035) when applying them in formulas.

Calculate the compound interest for a principal of $15,000 over 12 years at a 3.5% annual interest rate, compounded annually. This step-by-step guide uses the compound interest formula and explains the resulting amount of $22,671 and interest of $7,671. Suitable for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation