To purchase $$ \$ 11,800 $$ worth of restaurant equipment for her business, Jenny made a down payment of $$ \$ 1500 $$ and took out a business loan for the rest. After 2 years of paying monthly payments of $$ \$ 456.51 $$, she finally paid off the loan. (a) What was the total amount Jenny ended up paying for the equipment (induding the down payment and monthly payments)? (b) How much interest did Jenny pay on the loan?

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To solve the problem, we will break it down into two parts:

### Part (a): Total Amount Paid for the Equipment

1. **Calculate the total amount paid in monthly payments:**
   - Jenny made monthly payments of $$ \$ 456.51 $$ for 2 years.
   - The total number of months in 2 years is $$ 2 \times 12 = 24 $$ months.
   - Therefore, the total amount paid in monthly payments is:
     $$
     \text{Total Monthly Payments} = 456.51 \times 24
     $$

2. **Add the down payment to the total monthly payments:**
   - The down payment made by Jenny is $$ \$ 1500 $$.
   - The total amount paid for the equipment is:
     $$
     \text{Total Amount Paid} = \text{Total Monthly Payments} + \text{Down Payment}
     $$

Now, let's calculate the total amount paid in monthly payments and then the total amount paid for the equipment.

### Part (b): Interest Paid on the Loan

1. **Calculate the amount of the loan:**
   - The total cost of the equipment is $$ \$ 11,800 $$.
   - The amount of the loan is:
     $$
     \text{Loan Amount} = 11,800 - 1500
     $$

2. **Calculate the total interest paid:**
   - The total interest paid is the total amount paid minus the loan amount:
     $$
     \text{Interest Paid} = \text{Total Amount Paid} - \text{Loan Amount}
     $$

Now, let's perform the calculations for both parts.
Calculate the value by following steps:
- step0: Calculate:
  $$456.51\times 24$$
- step1: Multiply the numbers:
  $$10956.24$$
Calculate or simplify the expression $$ 11800 - 1500 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$11800-1500$$
- step1: Subtract the numbers:
  $$10300$$
Calculate or simplify the expression $$ 10956.24 + 1500 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$10956.24+1500$$
- step1: Add the numbers:
  $$12456.24$$
Calculate or simplify the expression $$ 12456.24 - 10300 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$12456.24-10300$$
- step1: Subtract the numbers:
  $$2156.24$$
### Part (a): Total Amount Paid for the Equipment

1. **Total Monthly Payments:**
   $$
   456.51 \times 24 = 10956.24
   $$

2. **Total Amount Paid:**
   $$
   \text{Total Amount Paid} = 10956.24 + 1500 = 12456.24
   $$

Thus, the total amount Jenny ended up paying for the equipment is **\$12,456.24**.

### Part (b): Interest Paid on the Loan

1. **Loan Amount:**
   $$
   \text{Loan Amount} = 11800 - 1500 = 10300
   $$

2. **Interest Paid:**
   $$
   \text{Interest Paid} = 12456.24 - 10300 = 2156.24
   $$

Therefore, the total interest Jenny paid on the loan is **\$2,156.24**.

### Summary of Results:
- **Total Amount Paid for the Equipment:** \$12,456.24
- **Total Interest Paid on the Loan:** \$2,156.24
Jenny paid a total of \$12,456.24 for the equipment, which includes a down payment of \$1,500 and \$10,956.24 in monthly payments. She paid \$2,156.24 in interest on the loan.

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