You deposit $500 each month into an account earning 5% interest compounded monthly.

How much total interest will you earn?

To calculate the total interest earned on a series of monthly deposits into an account with interest compounded monthly, we can use the formula for the future value of an annuity:

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

where:
- $FV$ is the future value of the annuity (total amount in the account after all deposits),
- $P$ is the monthly deposit ($500),
- $r$ is the monthly interest rate (annual rate divided by 12),
- $n$ is the total number of deposits (number of months).

Let's calculate:

1. **Determine the monthly interest rate:**
   \[
   r = \frac{5\%}{12} = \frac{0.05}{12} \approx 0.004167
   \]

2. **Assume the number of months, $n$, for a specified period** (let's calculate for 1 year and then for a more extended period like 5 years):
   - For 1 year: $n = 12$
   - For 5 years: $n = 60$

3. **Calculate the future value $FV$:**

   For 1 year:
   \[
   FV_{1\text{ year}} = 500 \times \left(\frac{(1 + 0.004167)^{12} - 1}{0.004167}\right)
   \]
   For 5 years:
   \[
   FV_{5\text{ years}} = 500 \times \left(\frac{(1 + 0.004167)^{60} - 1}{0.004167}\right)
   \]

4. **Subtract the total principal (total deposits) from the future value to find the interest earned.**

Let me calculate this for you.- **Total interest earned in 1 year:** $139.43
- **Total interest earned in 5 years:** $4,003.04

These calculations assume that you deposit $500 each month, and the interest is compounded monthly at a 5% annual rate.

Would you like further details or have any questions?

Here are 5 related questions you might find interesting:
1. How does the total interest change if the interest rate is 6% instead of 5%?
2. What would be the impact of increasing the monthly deposit to $600?
3. How much total interest would you earn in 10 years?
4. What is the effect of switching to a quarterly compounding interest instead of monthly?
5. How does the future value change if you make a one-time deposit instead of monthly deposits?

**Tip:** The power of compound interest is more noticeable over longer periods. The earlier you start saving, the more your money can grow!

Discover how to calculate total interest earned with monthly deposits and compound interest at a 5% annual rate. Understand the Future Value of Annuity formula and compute earnings for different time periods. Get insights on financial planning and compound interest benefits.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation