Answer :
Sure! Let's break it down step-by-step to find the required values:
1. Car price: [tex]$22,500.00 2. Down payment: $[/tex]2,000.00
3. Annual interest rate: 12%
4. Number of months for financing: 60 months
### Step 1: Calculating the amount to be financed
The amount Jane needs to finance is the car price minus the down payment.
[tex]\[ c = 22,500.00 - 2,000.00 = 20,500.00 \][/tex]
So, [tex]\( c = \$20,500.00 \)[/tex].
### Step 2: Calculating the monthly payment
To find the monthly payment, we use the formula for an amortizing loan, which is:
[tex]\[ \text{Monthly Payment} = P \times \left(\frac{r}{1 - (1 + r)^{-n}}\right) \][/tex]
where:
- [tex]\( P \)[/tex] is the principal amount (amount financed) = [tex]$20,500.00 - \( r \) is the monthly interest rate = \(\frac{12\%}{12} = 1\% = 0.01\) - \( n \) is the number of payments (months) = 60 Using these values, we get: \[ \text{Monthly Payment} = 20,500 \times \left(\frac{0.01}{1 - (1 + 0.01)^{-60}}\right) \] After calculating, we find the monthly payment is: \[ \text{Monthly Payment} \approx \$[/tex]456.01
\]
### Step 3: Calculating the total of payments
The total of payments over the 60 months is the monthly payment multiplied by the number of months:
[tex]\[ \text{Total of Payments} = 456.01 \times 60 = 27,360.67 \][/tex]
So, the total of payments is [tex]\(\$27,360.67\)[/tex].
### Summary:
- To the nearest penny, [tex]\( c =\$20,500.00 \)[/tex]
- Total of payments [tex]\( = \$27,360.67 \)[/tex]
- Total of payments [tex]\(\div\)[/tex] number of payments [tex]\( = \text{Monthly Payment} \approx \$456.01 \)[/tex]
These values are based on the calculations above.
1. Car price: [tex]$22,500.00 2. Down payment: $[/tex]2,000.00
3. Annual interest rate: 12%
4. Number of months for financing: 60 months
### Step 1: Calculating the amount to be financed
The amount Jane needs to finance is the car price minus the down payment.
[tex]\[ c = 22,500.00 - 2,000.00 = 20,500.00 \][/tex]
So, [tex]\( c = \$20,500.00 \)[/tex].
### Step 2: Calculating the monthly payment
To find the monthly payment, we use the formula for an amortizing loan, which is:
[tex]\[ \text{Monthly Payment} = P \times \left(\frac{r}{1 - (1 + r)^{-n}}\right) \][/tex]
where:
- [tex]\( P \)[/tex] is the principal amount (amount financed) = [tex]$20,500.00 - \( r \) is the monthly interest rate = \(\frac{12\%}{12} = 1\% = 0.01\) - \( n \) is the number of payments (months) = 60 Using these values, we get: \[ \text{Monthly Payment} = 20,500 \times \left(\frac{0.01}{1 - (1 + 0.01)^{-60}}\right) \] After calculating, we find the monthly payment is: \[ \text{Monthly Payment} \approx \$[/tex]456.01
\]
### Step 3: Calculating the total of payments
The total of payments over the 60 months is the monthly payment multiplied by the number of months:
[tex]\[ \text{Total of Payments} = 456.01 \times 60 = 27,360.67 \][/tex]
So, the total of payments is [tex]\(\$27,360.67\)[/tex].
### Summary:
- To the nearest penny, [tex]\( c =\$20,500.00 \)[/tex]
- Total of payments [tex]\( = \$27,360.67 \)[/tex]
- Total of payments [tex]\(\div\)[/tex] number of payments [tex]\( = \text{Monthly Payment} \approx \$456.01 \)[/tex]
These values are based on the calculations above.
