Determine the equivalent cash price of an item that can be purchased for $1950 down, and $2225 paid at the end of each year for 3 years if money is worth 4.62% simple interest.

To determine the equivalent cash price of the item, we need to calculate the present value of the payments made in the future. The present value is the amount you would need to pay today to be equivalent to those future payments when considering the interest rate.

### Given:
- Down payment: $ P_0 = \$1950 $
- Annual payment: $ P = \$2225 $ at the end of each year
- Number of years: $ n = 3 $
- Interest rate: $ r = 4.62\% $ per annum (simple interest)

### Step 1: Calculate the present value of the future payments.
The present value (PV) of each payment can be calculated using the formula for simple interest:

\[
PV = \frac{P}{1 + r \cdot t}
\]

where:
- $ P $ is the future payment,
- $ r $ is the interest rate per year,
- $ t $ is the time in years.

For the three payments:

1. **First Payment (t = 1 year)**:
   \[
   PV_1 = \frac{2225}{1 + 0.0462 \times 1} = \frac{2225}{1.0462} = \$2126.81
   \]

2. **Second Payment (t = 2 years)**:
   \[
   PV_2 = \frac{2225}{1 + 0.0462 \times 2} = \frac{2225}{1.0924} = \$2037.78
   \]

3. **Third Payment (t = 3 years)**:
   \[
   PV_3 = \frac{2225}{1 + 0.0462 \times 3} = \frac{2225}{1.1386} = \$1956.22
   \]

### Step 2: Add up the present values of the future payments and the down payment.
\[
\text{Total Present Value} = P_0 + PV_1 + PV_2 + PV_3
\]
\[
\text{Total Present Value} = 1950 + 2126.81 + 2037.78 + 1956.22 = \$8069.81
\]

### Conclusion:
The equivalent cash price of the item is **$8069.81**.

Would you like more details on this process or have any questions?

### Related Questions:
1. How would the equivalent cash price change if the interest rate were compounded annually?
2. What is the difference in present value if the payments were made semi-annually instead of annually?
3. How would the cash price differ if the down payment were increased to $2500?
4. What would be the equivalent cash price if the interest rate were 5% instead of 4.62%?
5. How does the number of payments (e.g., quarterly vs. yearly) affect the present value?

### Tip:
When dealing with multiple future payments, always calculate the present value of each payment separately and then sum them to find the equivalent cash price.

Learn how to calculate the equivalent cash price of an item using simple interest, based on a down payment of $1950 and annual payments of $2225 for 3 years at an interest rate of 4.62%. Understand the process of determining present values and their summation to find the total present value. Suitable for high school students learning about finance and simple interest calculations.

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