https://file.aiquickdraw.com/mathbot/file/17259391895913x7bsmls.jpg

The problem asks for the annual interest rate on a deposit that grows from $2700 to $3570.79 over 7 years, with interest compounded monthly. To solve this, we'll use the formula for compound interest:

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

Where:
- $ A $ is the final amount ($3570.79),
- $ P $ is the initial principal ($2700),
- $ r $ is the annual interest rate (which we need to find),
- $ n $ is the number of times the interest is compounded per year (12 for monthly compounding),
- $ t $ is the time in years (7 years).

We can rearrange the formula to solve for $ r $:

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

Let me calculate the interest rate for you.The annual interest rate for the account, compounded monthly, is approximately 4%.

Would you like further details or have any questions? Here are some related questions to explore:

1. How would the interest rate change if the interest were compounded quarterly instead of monthly?
2. What is the total interest earned over the 7 years on this deposit?
3. How can you calculate the effective annual rate (EAR) given a nominal rate with monthly compounding?
4. How long would it take for the deposit to double at the same interest rate?
5. What would the balance be after 10 years with the same interest rate and monthly compounding?

**Tip:** Always check if the interest is compounded more than once per year, as it affects the effective rate.

A deposit of $2700 in a savings account reaches a balance of $3570.79 after 7 years. The interest on the account is compounded monthly. What is the annual interest rate of the account? (Round your answer to the nearest whole number.)

Discover how to determine the annual interest rate of a savings account when $2700 grows to $3570.79 in 7 years with monthly compounding. This problem utilizes the compound interest formula to calculate growth.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation