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To calculate the cash price of the living room suite, we need to determine the present value (PV) of a simple annuity due. The details provided in the question are:

- **Semi-annual payment (PMT)**: $2560.00
- **Duration**: 8.5 years
- **Interest rate**: 14.5% compounded semi-annually
- **Number of payments per year**: 2 (since it's semi-annual payments)
- **Total number of payments**: $ 8.5 \times 2 = 17 $
- **Interest rate per period**: $ \frac{14.5\%}{2} = 7.25\% = 0.0725 $ per period

Since it's an **annuity due**, payments are made at the beginning of each period, so we will apply the present value formula for an annuity due.

The formula for the present value (PV) of an annuity due is:

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

Where:
- $ PMT $ is the payment amount,
- $ r $ is the interest rate per period,
- $ n $ is the total number of periods.

Let's plug in the numbers to find the cash price. I will compute this now.The cash price of the living room suite, based on the given annuity due contract, is approximately **$26,347.89**.

Would you like any additional details or further clarification? Here are five related questions you might find useful:

1. How would the cash price change if the interest rate was lower?
2. What is the difference between an ordinary annuity and an annuity due in calculations?
3. How would you calculate the future value of an annuity due in this scenario?
4. How would the present value change if payments were made quarterly instead of semi-annually?
5. What if Karina made a down payment—how would that affect the cash price?

**Tip**: Always distinguish between an ordinary annuity and an annuity due when performing present value calculations, as the payment timing significantly affects the result.

Karina paid for a living room suite over time, signing an installment contract that requires semi-annual payments of $2560.00 for 8.5 years. The first payment is made on the signing date, and interest is 14.5% compounded semi-annually. What was the cash price? (Hint: Simply calculate the PV of this Simple Annuity Due).

Learn how to calculate the cash price of a living room suite using the present value of an annuity due with semi-annual payments. This problem involves semi-annual payments of $2560 for 8.5 years at 14.5% interest compounded semi-annually. Suitable for finance and mathematics students.

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