Justine wants to save for retirement. She plans to put $130.00$130.00​ each month into an annuity that earns 2.5%2.5% for the next 2929​ years.  

How much will be in the account?  Round your final answer to the nearest cent.  Assume the interest rate stays the same while the account is open.

$$Future Value

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How much of the ending account balance is from deposits?

$$Total Deposited

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How much of the ending account balance comes from interest?

$$Interest

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To solve this problem, we'll calculate the future value of the annuity, the total amount deposited, and the interest earned over the 29 years.

### 1. Future Value of the Annuity

The future value of an annuity (FV) can be calculated using the formula:

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

Where:
- $ P $ = Monthly deposit = \$130.00
- $ r $ = Monthly interest rate = $\frac{2.5\%}{12} = 0.0020833$
- $ n $ = Total number of deposits = $29 \times 12 = 348$ months

Let's calculate the future value:

\[
FV = 130 \times \frac{(1 + 0.0020833)^{348} - 1}{0.0020833}
\]

I'll calculate this value.

\[
FV \approx 61,146.62
\]

So, the future value of the annuity is **\$61,146.62**.

### 2. Total Deposited

The total amount deposited is simply the monthly deposit multiplied by the number of deposits:

\[
\text{Total Deposited} = P \times n = 130 \times 348 = 45,240.00
\]

So, the total deposited is **\$45,240.00**.

### 3. Interest Earned

The interest earned is the difference between the future value of the annuity and the total deposited:

\[
\text{Interest} = FV - \text{Total Deposited} = 61,146.62 - 45,240 = 15,906.62
\]

So, the interest earned is **\$15,906.62**.

### Summary of Answers:
1. **Future Value:** \$61,146.62
2. **Total Deposited:** \$45,240.00
3. **Interest Earned:** \$15,906.62

Do you want more details or have any questions? Here are some related questions to consider:

1. How would the future value change if the interest rate was 3% instead of 2.5%?
2. What would happen to the future value if Justine deposited \$150 per month instead?
3. How much would Justine save in 20 years instead of 29 years at the same rate?
4. What is the impact on the future value if the interest is compounded weekly instead of monthly?
5. How would the interest earned change if the annuity was for 35 years instead of 29 years?

**Tip:** Starting to save early for retirement allows your investments to grow over time, benefiting from the power of compound interest.

Learn how to calculate the future value of an annuity with monthly deposits using compound interest. This problem involves calculating the future value, total amount deposited, and interest earned over a specified period. Explore detailed steps and formulas to solve similar financial calculations.

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