Blake has borrowed $30,000 on a 3-year note to buy a car. The loan requires equal monthly payments of principal and interest, with the first payment due one month after the loan is
Signed. The quoted interest rate is 7%. What will Blake's monthly payments be? Round your
Answer to the nearest dollar.

Question

Quizplus · Accepted Answer

Using the loan formula, we can find the amount of each monthly payment:
P = r(PV) / [1 - (1+r)^(-n)]
where P is the monthly payment, r is the monthly interest rate (0.07/12), PV is the present value (loan amount), and n is the number of payments (3 years x 12 months/year = 36 payments).

Plugging in the values, we get:
P = (0.00583 x 30000) / [1 - (1+0.00583)^(-36)]
P = 926.17

Rounding to the nearest dollar, we get:
P = $926

So Blake's monthly payments will be $926. To calculate the monthly payment, we can use the formula for an annuity:

PMT = R x PV / [1 - (1+R)^(-n)]

where PMT is the monthly payment, R is the monthly interest rate (which is the annual interest rate divided by 12), PV is the present value (the amount borrowed), and n is the number of payments (which is 3 years x 12 months/year = 36).

First, let's calculate the monthly interest rate:

R = 0.07/12 = 0.0058

Next, let's calculate the present value:

PV = $30,000

Finally, let's calculate the monthly payment:

PMT = 0.0058 x $30,000 / [1 - (1+0.0058)^(-36)]
PMT = $926.16

Rounded to the nearest dollar, the monthly payment is $926. Therefore, the best choice is B.

Blake Has Borrowed $30,000 on a 3-Year Note to Buy