You deposit​ $5000 in a savings plan at the end of each year for three years. The interest rate is​ 4% per year compounded annually.

Question content area bottom

Part 1

Find the interest.

​$enter your response here

​(Simplify your answer. Round to the nearest cent as​ needed.)

To solve this problem, we can calculate the total amount of money in the savings plan at the end of 3 years using the formula for the future value of an annuity (since you are depositing a fixed amount at the end of each year).

The formula for the future value of an annuity compounded annually is:

\[
FV = P \times \frac{(1 + r)^n - 1}{r}
\]

Where:
- $FV$ is the future value (the total amount at the end of 3 years).
- $P$ is the annual deposit ($5000).
- $r$ is the annual interest rate (4% = 0.04).
- $n$ is the number of years (3 years).

Let’s calculate the future value:

\[
FV = 5000 \times \frac{(1 + 0.04)^3 - 1}{0.04}
\]

Now, I'll compute this.The future value of your savings plan after 3 years is approximately \$15,608.

To find the total interest earned, we can subtract the total amount you deposited from the future value. You deposited \$5000 per year for 3 years, so the total deposit is:

\[
\text{Total Deposit} = 5000 \times 3 = 15000
\]

Now, the interest is:

\[
\text{Interest} = 15608 - 15000 = 608
\]

Thus, the interest earned is approximately **\$608**.

Would you like more details or have any questions? 

Here are some related questions:
1. How would the interest change if the deposit was made at the beginning of each year?
2. What would happen if the interest rate increased to 5%?
3. How would the future value change if the savings plan lasted 5 years instead of 3?
4. How does compound interest differ from simple interest in this case?
5. What would the interest be if the annual deposit was $6000?

**Tip:** The more frequently interest is compounded, the more you earn over time.

You deposit $5000 in a savings plan at the end of each year for three years. The interest rate is 4% per year compounded annually. Find the interest. (Simplify your answer. Round to the nearest cent as needed.)

Learn how to calculate the future value and interest earned in a 3-year savings plan with an annual deposit of $5000 and 4% interest compounded annually. Explore key financial concepts like compound interest and annuities. Suitable for high school students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation