Find the final amount of money in an account if
$5,300
is deposited at
3.5
%
interest compounded annually and the money is left for
10
years.

The final amount is $ . Round answer to 2 decimal places

The formula to calculate the final amount of money $ A $ in an account with compound interest is:

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

Where:
- $ P $ is the initial principal (the amount deposited),
- $ r $ is the annual interest rate (as a decimal),
- $ n $ is the number of times the interest is compounded per year,
- $ t $ is the number of years the money is left in the account.

Given:
- $ P = 5300 $,
- $ r = 3.5\% = 0.035 $,
- $ n = 1 $ (since the interest is compounded annually),
- $ t = 10 $ years.

Now, substitute the values into the formula:

\[
A = 5300 \left( 1 + \frac{0.035}{1} \right)^{1 \times 10}
\]

\[
A = 5300 \left( 1.035 \right)^{10}
\]

Let me calculate this for you.The final amount in the account after 10 years is **$7,476.17**.

Would you like further details or have any questions? Here are five related questions to expand on this concept:

1. How would the final amount change if the interest were compounded semi-annually instead of annually?
2. What would the final amount be if the deposit were left for 15 years instead of 10?
3. How much interest would be earned after 10 years?
4. What would happen if the interest rate increased to 5%?
5. How does continuous compounding affect the final amount?

**Tip:** The more frequently interest is compounded, the more money you accumulate, even if the interest rate stays the same.

Find the final amount of money in an account if $5,300 is deposited at 3.5% interest compounded annually and the money is left for 10 years. The final amount is $ . Round answer to 2 decimal places.

Calculate the final amount in an account after depositing $5,300 at 3.5% interest compounded annually over 10 years. Learn the step-by-step process using the compound interest formula A = P(1 + r/n)^(nt). Perfect 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