Find the future value of an ordinary annuity of $105/month for 10 years at 3.5%/year compounded monthly. (Round your answer to the nearest cent.)


To find the future value of an ordinary annuity, where payments are made at the end of each period, we use the future value of an ordinary annuity formula:

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

where:
- $ P $ is the payment amount per period,
- $ r $ is the interest rate per period,
- $ n $ is the total number of payments.

Given values:
- Monthly payment, $ P = 105 $
- Annual interest rate, $ 3.5\% $, so the monthly interest rate $ r = \frac{0.035}{12} $
- Total number of payments, $ n = 10 \times 12 = 120 $

### Step 1: Convert the interest rate to a monthly rate
\[
r = \frac{0.035}{12} \approx 0.00291667
\]

### Step 2: Calculate $ (1 + r)^n - 1 $
\[
(1 + 0.00291667)^{120} - 1 \approx 0.422925
\]

### Step 3: Substitute values into the formula
\[
FV = 105 \times \frac{0.422925}{0.00291667}
\]
\[
FV \approx 105 \times 144.9226
\]
\[
FV \approx 15216.88
\]

### Final Answer
The future value of the annuity is approximately **$15,216.88**.

Would you like further details on any steps? 

Here are some related questions:
1. How does compounding frequency affect annuity future values?
2. What is the difference between an ordinary annuity and an annuity due?
3. How would a change in interest rate impact this future value calculation?
4. How does the future value formula differ for other compounding periods (e.g., quarterly)?
5. What if payments were made at the beginning of each period (annuity due)?

**Tip:** Always remember, increasing the compounding frequency (like monthly vs. annually) generally increases the future value due to more frequent interest application.

Find the future value of an ordinary annuity of $105/month for 10 years at 3.5%/year compounded monthly. (Round your answer to the nearest cent.)

Calculate the future value of an ordinary annuity with a $105 monthly payment for 10 years at an interest rate of 3.5% per year, compounded monthly. This detailed solution provides a step-by-step guide to annuity and compound interest concepts, ideal for advanced high school and college-level students.

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