Jackson deposited $125 a month into an account earning 9.0% compounded monthly for 17 years. He left the accumulated amount for another 2 years at the same interest rate. How much total interest did he earn?

To solve this problem, we need to approach it in two parts:

1. **Calculate the accumulated amount after 17 years of monthly deposits.**
2. **Calculate the interest earned on that accumulated amount during the additional 2 years.**

### Step 1: Future Value of Monthly Deposits for 17 Years

The formula for the future value of an annuity with monthly compounding is:

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

where:
- $ P = 125 $ (monthly deposit),
- $ r = 0.09 $ (annual interest rate),
- $ n = 12 $ (compounded monthly),
- $ t = 17 $ years.

Plugging in these values:

\[
FV = 125 \times \frac{(1 + \frac{0.09}{12})^{12 \times 17} - 1}{\frac{0.09}{12}}
\]

### Step 2: Calculate Future Value of Accumulated Amount for an Additional 2 Years

Let’s denote the future value after 17 years as $ A_{17} $.

Now, let $ A_{17} $ grow for an additional 2 years at the same interest rate compounded monthly:

\[
A_{19} = A_{17} \times \left(1 + \frac{r}{n}\right)^{n \times 2}
\]

### Step 3: Calculate Total Interest Earned

The total interest earned will be:

\[
\text{Total Interest} = A_{19} - (125 \times 12 \times 17)
\]

I'll calculate each part step-by-step.### Solution Summary

1. **Accumulated Amount after 17 Years of Deposits (FV_17):** $59,864.78
2. **Accumulated Amount after an Additional 2 Years (FV_19):** $71,623.03
3. **Total Interest Earned:** $46,123.03

Jackson earned a total interest of **$46,123.03** over the 19 years.

Would you like more details on each step, or do you have questions?

### Additional Related Questions
1. How would the interest change if the compounding frequency was quarterly instead of monthly?
2. What would happen to the total interest if Jackson had deposited $150 monthly instead?
3. How much total interest would be earned if the rate was reduced to 6% compounded monthly?
4. If Jackson increased his monthly deposit to $200 in the last 5 years, what would the new balance be?
5. How much principal was deposited over the entire 19 years?

### Tip
Compounding frequency can significantly impact the final amount. More frequent compounding (e.g., monthly vs. annually) generally yields a higher balance due to faster reinvestment of interest.

Explore how to calculate the total interest earned on monthly deposits of $125 into an account with 9% annual interest compounded monthly over 17 years, followed by additional compounding for 2 years. Learn to apply key formulas like the Future Value of Annuity and Compound Interest for accurate financial forecasting. Suitable for 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