How to calculate the present value of this?

My question is the following task: You are purchasing a new car. The price is $ 18,239. You pay $ 2,000 now and the rest, monthly, in a 4-year loan. The car dealer is offering a sales promotion when: 1) You will receive a refund check of $ 1000 and now the annual interest rate of the loan is 11.9% or 2) The annual interest rate on the loan is 1.9%, but no discount. Compare the two options for calculating the present value of each option, assuming the discount rate is 8%. That is a better deal? I may use Excel, but I do not know where to begin When comparing both scenarios, more or less a PV PV represent a better deal? I guess less PV?

The current value will future payments you make discount for the discount rate. This is the same as saying how much money is needed to put in the bank today to an interest rate that equals the discount rate (8%) to have the amount of your goal in 4 years. Scenario 1 Calculate Target Amount 2000 Down Payment loan repayment amount = 18.239 – 2.000 = 16.239 at a compounded annual return of 11.9% 16,239 X 1,119 = 18,171 (first year) 18,171 X 1.119 = 20,334 (second year) 20,334 X 1.119 = 22,754 (third years) 22,754 X 1.119 = 25,461 (fourth year), but it's better doing it this way 16,239 X (1.119) ^ 4 = 16,239 x 1.5677 = 25,457 (the difference is due to errors rounding) Therefore, on a line compounded interest of 11.9% a year without any compensation for the money you're paying monthly pay was 25,457 instead of 16,239 you owe. This is the target (future) value. If you are paying this amount in four years, you will pay 25,457 / 4 = 6,364.25 per year now to calculate the discount rate (present value). How much money is needed to put in a bank with an interest rate of 8% in order to have 25,457 in 4 years? (You need to "devalue" the money at 8% per annum compound). This is the same as the calculation of interest, but in reverse. Year 1 – Payment in fare 6364.25 Off = 1 / (1 + 0.8) ^ 1 = 6,364.25 X 0.9259 = 5,892.66 Year 2 – Payment of 6364.25 in the discount rate = 1 / (1 + 0.8) ^ 2 = 6,364.25 X 0.8573 = 5456.07 Year 3 – Payment of 6364.25 in the discount rate = 1 / (1 + 0.8) ^ 3 = 6,364.25 x 0.7938 = 5051.94 Year 4 – Payment 6364.25 Discount Rate = 1 / (1 + 0.8) ^ 4 = 6,364.25 X 0.7350 = 4,677.72 Therefore the money you pay more than 4 years, reducing its value at present is 5,892.66 + 5,456.07 + 5,051.94 + 4,677.72 = 23,078.39 Add 2000 payment = 25,078.39 and subtract the cash rebate of 1,000 = 24,078.39 Therefore, the current value for vehicles the 18,239 that are buying is really 24,078.39 to scenario 1. The same type of calculation has to be done for Scenario 2, but has no account for any cash rebate in the final calculation.

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