Ordinary annuities: What is the present value of $5000 for one year with an annual interest rate of 1.2% (APR with monthly compounding)

To find the present value of an ordinary annuity, we can use the present value formula for annuities. However, since you mentioned monthly compounding and an annual interest rate (APR), we need to adjust for this.

### Given:
- Payment ($ P $) = $5,000
- Interest rate ($ i $) = 1.2% annually, compounded monthly
- Time period ($ t $) = 1 year (or 12 months)

### Steps:
1. **Monthly interest rate**: Since the interest is compounded monthly, we divide the annual rate by 12.
   \[
   i_{monthly} = \frac{1.2\%}{12} = 0.001 = 0.1\%
   \]

2. **Number of periods**: Over one year, with monthly payments, there are 12 periods.
   \[
   n = 12
   \]

3. **Present value formula**:
   The present value ($ PV $) of an ordinary annuity can be calculated using the formula:
   \[
   PV = P \times \frac{1 - (1 + i_{monthly})^{-n}}{i_{monthly}}
   \]
   Where:
   - $ P $ = payment per period ($5,000)
   - $ i_{monthly} $ = monthly interest rate
   - $ n $ = number of periods

Let me calculate that for you.The present value of receiving $5,000 monthly for one year, with an annual interest rate of 1.2% compounded monthly, is approximately **$59,611.81**.

Would you like more details or have any questions?

Here are five related questions:
1. How would the present value change with a higher interest rate?
2. What happens to the present value if the annuity lasts for more than one year?
3. How does monthly compounding differ from annual compounding for this calculation?
4. What is the future value of the same annuity after one year?
5. How would the present value be different if payments were made quarterly?

**Tip**: When dealing with monthly compounding, always remember to adjust both the interest rate and the number of periods accordingly.

Ordinary annuities: What is the present value of $5000 for one year with an annual interest rate of 1.2% (APR with monthly compounding)?

Learn how to calculate the present value of an ordinary annuity receiving $5,000 annually, with a 1.2% annual interest rate and monthly compounding. Includes key concepts like compound interest and the present value formula. Suitable for college-level finance students.

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