Suppose that you are thinking about buying a car and have narrowed down your choices to two options.
The new-car option: The new car costs $29 comma 000 and can be financed with a three-year loan at 5.15%.
The used-car option: A three-year old model of the same car costs $15 comma 000 and can be financed with a five-year loan at 6.44%.
What is the difference in monthly payments between financing the new car and financing the used car? Use PMT equals StartStartFraction Upper P left parenthesis StartFraction r Over n EndFraction right parenthesis OverOver left bracket 1 minus left parenthesis 1 plus StartFraction r Over n EndFraction right parenthesis Superscript negative nt right bracket EndEndFraction
.
Question content area bottom
Part 1
The difference in monthly payments between financing the new car and financing the used car is $

Question

contestada

Respuesta :

N0seeee N0seeee · Answer 1 · 2024-03-08T21:39:22+01:00

For the new car:

PMT = P * (r/n) / (1 - (1 + r/n)^(-nt))

P = $29,000

r = 5.15% = 0.0515

n = 12 (number of payments per year)

t = 3 years

PMT (new car) = $29,000 * (0.0515/12) / (1 - (1 + 0.0515/12)^(-12*3))

PMT (new car) ≈ $867.53

For the used car:

P = $15,000

r = 6.44% = 0.0644

n = 12

t = 5 years

PMT (used car) = $15,000 * (0.0644/12) / (1 - (1 + 0.0644/12)^(-12*5))

PMT (used car) ≈ $293.60

Therefore, the difference in monthly payments between financing the new car and financing the used car is:

$867.53 - $293.60 = $573.93