To buy a car,you are given two options.Option 1 is to pay $20,000 cash today.Option 2 is to make monthly payments of $500 for as long as necessary,first payment made today.If the dealer charges interest at j₁₂ = 5.4%,how many payments are needed,including the very first one,if the final payment is increased by a balloon payment? A)42 B)43 C)44 D)45

Question

Quizplus · Accepted Answer

Using the present value formula, we can find that the total cost of option 2 with monthly payments is:

PV = (500/0.0045)(1-1/1.0045^Nx12) + 20000/(1.0045^(Nx12))

where Nx12 is the number of monthly payments needed and PV is the present value of all the payments.

To find the number of payments needed with a balloon payment, we can set PV equal to 20000 and solve for Nx12.

20000 = (500/0.0045)(1-1/1.0045^Nx12) + 20000/(1.0045^(Nx12))

Solving this equation using a spreadsheet or calculator, we get Nx12 = 42.95, which means we need 43 payments including the very first one. Therefore, option B is the best choice since it requires fewer overall payments and a lower total cost compared to option 1.

To Buy a Car,you Are Given Two Options