Freddie bought a car worth $42,000 today. He was required to make a 15% down payment. The remainder was to be paid as a monthly payment over the next 12 months with the first payment due at t = 1. Given that the interest rate is 8% per annum compounded monthly, what is the approximate monthly payment?
The Professor solved it like this:
Loan amount = 85% of $42,000 = 0.85 x 42,000 = $35,700 PV = $35,700 N = 12 I/Y = 8/12% FV = 0 CPT PMT PMT = $3,105.48
Isnt it like this?
PV = 6,300 (since that is the initial down payment at time 0)
FV = 35,700 (that is the amount I will be left paying in the future)
N = 12
I/Y = 8/12
CPT PMT
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If you agree with the Professor, can you please explain to me what the calculator is trying to solve/understanding if you just plug in a PV and no FV? What are you calculating the Pmt on if FV = 0??
You need to find the PV of monthly payments that equates the value of your car today discounted at 8% compounded monthly. Since you pay 6300 today, it has no time value impact. It is simply deducted from the total amount you need to pay for the car. 35 700 is not a future value because that’s the value of the car in the present.
What you’re trying to calculate is what payment needs to be made each month to make the loan amount $0 in 12 months. Because Freddie made a down payment of $6,300 on the car, it reduces the size of the loan he needs to $35,700. The value of the loan that you’re trying to pay down is the PV ($35,700). Your FV of the calculation is 0 because he wants to pay off the loan in 12 months, so that’s why you set FV=0 (why would you want it to be higher than 0 unless stated otherwise?). Because it’s monthly, you multiply N by 12 and divide I/Y by 12.