Question

You want to buy a car, and a local bank will lend you $25,000. The loan will be fully amortized over 5 years (60 months), and the nominal interest rate will be 4% with interest paid monthly. What will be the monthly loan payment? What will be the loan's EAR? Do not round intermediate calculations. Round your answer for the monthly loan payment to the nearest cent and for EAR to two decimal places.

Answer 1

Monthly payment: 460.41 dollars

Effective rate: 4.07%

Step-by-step explanation:

we will calculate the PTM of an annuity of 25,000 over 5 year at 4%

`PV / (1-(1+r)^(-time) )/(rate) = C\\`

PV $25,000.00

time 60

rate 0.003333333

`25000 / (1-(1+0.003333)^(-60) )/(0.003333) = C\\`

C $ 460.413

Now we need to know the effective rate, which is the same as 4% compounding monthly:

`(1+0.04/12)^(60) = (1+ r_e)^(5)\\r_e = \sqrt[5]{(1+0.04/12)^(60)} - 1`

effective rate = 0.040741543 = 4.07%