Question

Annuity Payment and EAR

You want to buy a car, and a local bank will lend you $35,000. The loan would be fully amortized over 5 years (60 months), and the nominal interest rate would be 10% with interest paid monthly. What is the monthly loan payment? Do not round intermediate calculations. Round your answer to the nearest cent.
$   

What is the loan's EFF%? Round your answer to two decimal places.
%

Answer 1

Given

Rate = 10%

Monthly rate = 0.10/12

                      = 0.00833

Number of periods = 5*12

                               = 60

Present value of loan = $35,000

The monthly loan payment and loan EAR or EFF can be computed by using the PMT formula and EAR formula in the excel sheet as follows:

EAR or EFF = {1 + (Rate/12)¹² ]– 1}

1 Computation of monthly Loan payment and EAR 2 Rate =10%/12 3 Nper =5*12 4 PV - 35000 5 6 Monthly Payment of loan =PMT(B2,B3,B4) 8 Loan EAR =((1+B2)^12) - 1

The monthly loan payment and EAR or EFF is computed as follows by using the above formula in the excel sheet:

1 Computation of monthly Loan payment and EAR 2 Rate 0.008333333 3 Nper -35000 4 PV 5 6 Monthly Payment of loan 743.65 8 Loan EAR 10.47%

Thus,

Monthly payment of loan = $743.65

= $744 (approx.)

Loan EAR = 10.47%

Note: The loan EFF is assumed as loan EAR (Effective annual rate).