OHaganBooks.com has just introduced a retirement package for its employees. Under the annuity plan operated by Sleepy Hollow, the monthly contribution by the company on behalf of each employee is $700. Each employee can then supplement that amount through payroll deductions. The current rate of return of Sleepy Hollow's retirement fund is 7.5%.
Jane Callahan, the website developer at OHaganBooks.com, plans to retire in 10 years. She contributes $1,000 per month to the plan (in addition to the company contribution of $700). Currently, there is $70,000 in her retirement annuity. How much (to the nearest dollar) will it be worth when she retires? (Assume interest is compounded monthly.)

To determine how much Jane Callahan's retirement annuity will be worth when she retires, we need to calculate the future value of two components: 

1. **The existing balance** ($70,000).
2. **The monthly contributions** ($1,700) over the next 10 years.

The future value formula for compound interest is:

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

Where:
- $ FV $ is the future value of the annuity.
- $ P $ is the present value or current amount ($70,000).
- $ C $ is the total monthly contribution ($1,700 = $700 from the company + $1,000 from Jane).
- $ r $ is the annual interest rate (7.5% or 0.075).
- $ t $ is the number of years (10 years).
- $ n $ is the number of times interest is compounded per year (12 for monthly compounding).

### Step-by-Step Calculation:

#### 1. Future Value of Current Balance:
We use the first part of the formula:

\[
FV_1 = 70,000 \times \left(1 + \frac{0.075}{12}\right)^{12 \times 10}
\]

\[
FV_1 = 70,000 \times (1.00625)^{120}
\]

\[
FV_1 \approx 70,000 \times 2.10568
\]

\[
FV_1 \approx 147,397.60
\]

#### 2. Future Value of Monthly Contributions:
For the monthly contributions, we use the second part of the formula:

\[
FV_2 = \frac{1,700 \times \left( \left(1 + \frac{0.075}{12}\right)^{12 \times 10} - 1 \right)}{\frac{0.075}{12}}
\]

\[
FV_2 = \frac{1,700 \times \left( 2.10568 - 1 \right)}{0.00625}
\]

\[
FV_2 = \frac{1,700 \times 1.10568}{0.00625}
\]

\[
FV_2 \approx \frac{1,700 \times 1.10568}{0.00625}
\]

\[
FV_2 \approx 300,146.77
\]

#### 3. Total Future Value:
The total future value is the sum of the future value of the current balance and the future value of the monthly contributions:

\[
FV = 147,397.60 + 300,146.77
\]

\[
FV \approx 447,544
\]

### Final Answer:
Jane Callahan’s retirement annuity will be worth approximately **$447,544** when she retires.

---

Would you like more details on the calculation or any part of this explained further?

### Related Questions:
1. How would the result change if the interest rate were 8% instead of 7.5%?
2. What if Jane decides to contribute $1,200 per month instead of $1,000?
3. How does increasing the compounding frequency (e.g., to daily) affect the outcome?
4. What if Jane had an initial balance of $100,000 instead of $70,000?
5. How would the outcome differ if Jane retires in 15 years instead of 10?

#### Tip:
The more frequently interest is compounded, the greater the impact of compound interest on your investment. For the same rate, increasing compounding frequency leads to higher returns.

OHaganBooks.com has just introduced a retirement package for its employees. Under the annuity plan operated by Sleepy Hollow, the monthly contribution by the company on behalf of each employee is $700. Each employee can then supplement that amount through payroll deductions. The current rate of return of Sleepy Hollow's retirement fund is 7.5%. Jane Callahan, the website developer at OHaganBooks.com, plans to retire in 10 years. She contributes $1,000 per month to the plan (in addition to the company contribution of $700). Currently, there is $70,000 in her retirement annuity. How much (to the nearest dollar) will it be worth when she retires? (Assume interest is compounded monthly.)

Calculate the future value of Jane Callahan's retirement annuity using a 7.5% interest rate and monthly contributions. This detailed solution explains how to find the future value of both her current balance of $70,000 and her monthly contributions of $1,700, compounded monthly over 10 years. Perfect for students in Grades 10-12 learning about compound interest and annuities.

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