Find the present value of an annuity due that pays $4000 at the beginning of each quarter for the next 8 years. Assume that money is worth 5.4%, compounded quarterly. (Round your answer to the nearest cent.)


To find the present value of an **annuity due** where payments are made at the beginning of each period, we use the following formula:

\[
PV = P \times \left[ \frac{1 - (1 + i)^{-n}}{i} \right] \times (1 + i)
\]

Where:
- $ PV $ is the present value of the annuity due,
- $ P $ is the payment amount per period,
- $ i $ is the interest rate per period,
- $ n $ is the total number of periods.

### Step 1: Identify the variables
- $ P = 4000 $ (payment at the beginning of each quarter),
- The annual interest rate is 5.4%, so the quarterly interest rate $ i = \frac{5.4\%}{4} = \frac{0.054}{4} = 0.0135 $,
- The number of quarters over 8 years is $ n = 8 \times 4 = 32 $.

### Step 2: Plug the values into the formula

Now, let's calculate the present value using the given values.The present value of the annuity due is **$104,776.89**.

Would you like a detailed breakdown of the steps or further clarifications?

Here are 5 related questions:
1. How does an annuity due differ from an ordinary annuity in terms of present value?
2. What happens to the present value if the interest rate increases to 6%?
3. How would the present value change if the payments were made at the end of each period (ordinary annuity)?
4. How is the formula for annuity due derived from the ordinary annuity formula?
5. What is the future value of the same annuity if compounded quarterly?

**Tip:** Annuities due result in a higher present value than ordinary annuities because payments are made at the beginning of each period, providing extra time for interest accumulation.

Find the present value of an annuity due that pays $4000 at the beginning of each quarter for the next 8 years. Assume that money is worth 5.4%, compounded quarterly. (Round your answer to the nearest cent.)

Calculate the present value of an annuity due that pays $4000 at the beginning of each quarter for 8 years, with a 5.4% interest rate compounded quarterly. This problem involves key financial concepts such as the time value of money, present value, and compound interest.

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