A DVD component set is offered for sale for ₱6, 500 down payment and ₱1, 750 every end of each month for
the balance, for 2 years. If the interest rate is 4 ½% compounded monthly, what is the cash price equivalent
of the set?

To find the cash price equivalent of the DVD component set, we need to determine the present value (PV) of all the payments, including the down payment and the monthly installments. The problem involves a down payment followed by an annuity (the monthly payments). 

Here are the steps to solve the problem:

### Given:
- **Down payment**: ₱6,500
- **Monthly payment (PMT)**: ₱1,750
- **Number of payments (n)**: 2 years × 12 months/year = 24 months
- **Interest rate per month (i)**: \( \frac{4.5\%}{12} \) = 0.375% = 0.00375

### Steps:
1. **Calculate the present value of the annuity (monthly payments):**
   \[
   PV_{\text{annuity}} = PMT \times \frac{1 - (1 + i)^{-n}}{i}
   \]
   Plugging in the values:
   \[
   PV_{\text{annuity}} = 1,750 \times \frac{1 - (1 + 0.00375)^{-24}}{0.00375}
   \]

2. **Add the down payment to get the total present value (cash price equivalent):**
   \[
   \text{Cash Price Equivalent} = PV_{\text{annuity}} + \text{Down payment}
   \]

Let's calculate the present value of the annuity and then add the down payment.The cash price equivalent of the DVD component set is approximately **₱46,593.65**.

Would you like further details or have any questions?

Here are 5 related questions to consider:

1. How would the cash price change if the interest rate were 6% compounded monthly?
2. What would be the cash price if the monthly payments were ₱2,000 instead of ₱1,750?
3. How would

Learn how to calculate the cash price equivalent of a DVD component set with a down payment of ₱6,500 and monthly payments of ₱1,750 over 2 years at an interest rate of 4.5% compounded monthly. Understand the concept of present value and annuities in finance.

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