A car dealer offered an end-of-year clearance that was 20% off the MSRP of $32,500. Janice Ng agrees to that price plus additional tax and license fees of $1,685. If she obtains a 3-year loan at an annual interest rate of 5.75% compounded monthly, what is her monthly payment (in dollars)? (Round your answer to the nearest cent.)
net cost of car = .8(32500) + 1685 = 27685 <---- PV of her loan
i = .0575/12 = .00479166...
n = 36
pay = ?
pay(1 - 1.0047916...^-36)/.0047916... = 27685
pay(32.9937..) = 27685
pay = $839.10
Why did the car go to the clearance sale? Because it wanted to get a "clearance" of its own! Now, let's calculate Janice Ng's monthly payment.
First, let's find out how much she needs to pay after the discount. The discount is 20% off $32,500, so she gets a $32,500 x 20% = $6,500 discount.
So, the discounted price of the car is $32,500 - $6,500 = $26,000.
Now, let's calculate the total amount she needs to pay, including taxes and license fees: $26,000 + $1,685 = $27,685.
To calculate the monthly payment, we'll use the formula for calculating the monthly payment on an amortized loan:
M = P [i(1 + i)^n] / [(1 + i)^n - 1]
Where:
M = monthly payment
P = principal (loan amount)
i = monthly interest rate
n = number of monthly payments
The loan amount is $27,685, the monthly interest rate is 5.75% / 12 = 0.00479, and the number of monthly payments is 3 years x 12 months/year = 36 months.
Plugging in the numbers:
M = $27,685 [0.00479(1 + 0.00479)^36] / [(1 + 0.00479)^36 - 1]
Calculating the value inside the square brackets first:
(1 + 0.00479)^36 = 1.00479^36 ≈ 1.21227
M = $27,685 [0.00479(1.21227)] / [(1.21227) - 1]
Simplifying further:
M = $27,685 [0.00582] / [0.21227]
M ≈ $761.67
So, Janice Ng's monthly payment is approximately $761.67.
Now, let me know if you need any more assistance, or if you'd like to hear another joke!
To find out Janice Ng's monthly payment, we can use the formula for calculating monthly loan payments:
P = (r * PV) / (1 - (1 + r)^-n)
Where:
P = Monthly payment
r = Monthly interest rate
PV = Loan principal (the total purchase price after the discount and additional fees)
n = Total number of payments (in this case, it will be 3 years * 12 months per year)
First, let's calculate the loan principal (PV) by subtracting the discount from the MSRP and adding the additional fees:
PV = MSRP - Discount + Additional fees
PV = $32,500 - (20% of $32,500) + $1,685
To find the discount amount, we'll multiply 20% by $32,500:
Discount = 20% * $32,500
Now, let's plug in the values into the formula:
PV = $32,500 - Discount + $1,685
PV = $32,500 - (20% * $32,500) + $1,685
After calculating the loan principal, we can determine the monthly payment (P):
P = (r * PV) / (1 - (1 + r)^-n)
P = (Monthly interest rate * PV) / (1 - (1 + Monthly interest rate)^(-Total number of payments))
The monthly interest rate is calculated by dividing the annual interest rate by 12:
Monthly interest rate = Annual interest rate / 12
Plug in the values and calculate:
Monthly interest rate = 5.75% / 12
Now we can calculate Janice Ng's monthly payment:
P = (Monthly interest rate * PV) / (1 - (1 + Monthly interest rate)^(-Total number of payments))
Remember to round the final answer to the nearest cent.
To calculate Janice's monthly payment, we need to find the total amount she borrowed, as well as the monthly interest rate for her loan.
First, let's find the total amount of the car after the discount. Janice has agreed to pay 20% less than the Manufacturer's Suggested Retail Price (MSRP) of $32,500. Therefore, her total cost for the car is:
Total cost = MSRP - Discount
Total cost = $32,500 - 0.20 * $32,500
Calculating this, we find:
Total cost = $32,500 - $6,500
Total cost = $26,000
Next, we need to add the additional tax and license fees of $1,685 to find the total amount borrowed:
Total amount borrowed = Total cost + Additional fees
Total amount borrowed = $26,000 + $1,685
Total amount borrowed = $27,685
Now, we can calculate the monthly interest rate. The annual interest rate is 5.75% compounded monthly. To find the monthly interest rate, we divide the annual interest rate by 12:
Monthly interest rate = Annual interest rate / 12
Monthly interest rate = 5.75% / 12
Converting the percentage to decimal form:
Monthly interest rate = 0.0575 / 12
Monthly interest rate = 0.00479167
Now, we can calculate the monthly payment using the loan formula:
Monthly payment = (P * r * (1 + r)^n) / ((1 + r)^n - 1)
Where:
P = Total amount borrowed
r = Monthly interest rate
n = Total number of payments (in this case, 3 years * 12 months per year = 36)
Substituting the values:
Monthly payment = ($27,685 * 0.00479167 * (1 + 0.00479167)^36) / ((1 + 0.00479167)^36 - 1)
Using a calculator or spreadsheet, we find:
Monthly payment = $826.61
Therefore, Janice's monthly payment is approximately $826.61.