Sure, let's work through this step-by-step to find the monthly payments for a simple interest loan with the provided parameters.
### Step 1: Understand the Key Information
The key information provided includes:
- Principal amount: $3,000
- Annual interest rate: 15%
- Number of monthly installments: 12
### Step 2: Determine Monthly Interest Rate
Given the annual interest rate is 15%, we need to convert this to a monthly interest rate.
[tex]\[ \text{Monthly Interest Rate} = \frac{\text{Annual Interest Rate}}{12} \][/tex]
So,
[tex]\[ \text{Monthly Interest Rate} = \frac{15\%}{12} = 0.0125 \][/tex]
### Step 3: Calculate the Monthly Interest Component
The interest for the principal amount each month can be calculated by multiplying the principal by the monthly interest rate.
[tex]\[ \text{Monthly Interest Component} = \text{Principal} \times \text{Monthly Interest Rate} \][/tex]
[tex]\[ \text{Monthly Interest Component} = 3000 \times 0.0125 = 37.5 \][/tex]
### Step 4: Calculate the Principal Repayment Per Month
The principal repayment part of the monthly payment is simply the total principal divided by the number of months.
[tex]\[ \text{Principal Repayment Per Month} = \frac{\text{Principal}}{\text{Number of Months}} \][/tex]
[tex]\[ \text{Principal Repayment Per Month} = \frac{3000}{12} = 250 \][/tex]
### Step 5: Calculate Total Monthly Payment
Add the monthly interest component to the principal repayment per month to get the total monthly payment.
[tex]\[ \text{Monthly Payment} = \text{Principal Repayment Per Month} + \text{Monthly Interest Component} \][/tex]
[tex]\[ \text{Monthly Payment} = 250 + 37.5 = 287.5 \][/tex]
### Step 6: Choose Your Answer
Based on the calculations, the correct amount of the monthly payments is:
[tex]\[ \boxed{287.50} \][/tex]
