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 6% 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

Present value (PV) = $25,000

Interest rate (r) = 6%

Number of years (n) = 5 years

Number of compounding periods within a year (m) = 1 2

Monthly payment (A ) = ?

PV = A(1 - (1 + r/m) -nm)

r/m

$25,000 = A(1 -(1 + 0.06/12)-5x12)

0.06/2

$25,000 = A(1 - (1 +0.005)-60)

0.05

$25,000 = A(1 -(1.005)-60)

0.005

$25,000 = A(51.72556075)

$25,000 = A

51.72556075

A = $483

EAR = (1 + r/m)m - 1

EAR = ((1 + 0.06/12)12 - 1

EAR = (1 + 0.005)12 - 1

EAR = 0.0617 = 6.17%

Step-by-step explanation:

In this case, we need to calculate the monthly loan payment by applying amortization formula as shown above. The amount borrowed, interest rate, number of years and number of compounding periods within a year have been given with the exception of monthly loan payment. Thus, we will make the monthly loan payment the subject of the formula.

In the second case, the effective interest rate is calculated using the formula (1 + r/m)m - 1, where r is the interest rate and m is the number of compounding periods within a year.