**amount of annuity $32,000**

**Interest rate 7%**

**Period**​ (years) 4   Calculate the present value of the annuity assuming that it is

​(1)  An ordinary annuity.

​(2)  An annuity due.




To calculate the present value (PV) of an annuity, we use the following formulas:

### 1. **Ordinary Annuity:**
For an ordinary annuity, the payments are made at the end of each period. The formula for the present value is:

\[
PV_{\text{ordinary}} = A \times \left( \frac{1 - (1 + r)^{-n}}{r} \right)
\]

Where:
- $ A $ = amount of annuity per period = \$32,000
- $ r $ = interest rate per period = 7% = 0.07
- $ n $ = number of periods = 4 years

### 2. **Annuity Due:**
For an annuity due, the payments are made at the beginning of each period. The present value formula is similar to the ordinary annuity but with a slight adjustment:

\[
PV_{\text{due}} = A \times \left( \frac{1 - (1 + r)^{-n}}{r} \right) \times (1 + r)
\]

I will calculate the present values for both the ordinary annuity and the annuity due.

Let's compute the results.### The present values of the annuity are as follows:

1. **Ordinary Annuity:** \$108,390.76
2. **Annuity Due:** \$115,978.11

Would you like further explanation or have any questions about these calculations?

Here are some related questions you might want to consider:
1. How would the present value change if the interest rate was different?
2. What happens to the present value if the period is extended to 6 years?
3. How does an ordinary annuity differ from an annuity due in financial applications?
4. Can you calculate the future value of these annuities after 4 years?
5. What impact does compounding frequency (monthly, quarterly, etc.) have on annuity calculations?

**Tip:** Annuity due will always have a higher present value than an ordinary annuity, given the same interest rate and payment amount, because payments are made earlier.

amount of annuity $32,000, Interest rate 7%, Period (years) 4. Calculate the present value of the annuity assuming that it is (1) An ordinary annuity. (2) An annuity due.

Calculate the present value of a $32,000 annuity with a 7% interest rate over 4 years. Explore the differences between ordinary annuity and annuity due, using the time value of money principle. Find out how to apply key formulas for accurate financial forecasting.

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