A commercial bank will loan you $20,000 for four years to buy a car. The loan must be repaid in 48 equal monthly payments. The annual interest rate on the loan is 6.00 percent of the unpaid balance. How large are the monthly payments?

Monthly payment = $469.701

Explanation:

Loan Amortization: A loan repayment method structured such that a series of equal periodic installments will be paid for certain number of periods to offset both the loan principal amount and the accrued interest.  

The monthly equal installment is calculated as follows:  

Monthly equal installment= Loan amount/Monthly annuity factor  

Loan amount = 20,000

Monthly annuity factor  =

=( 1-(1+r)^(-n))/r  

r- Monthly interest rate (r)  

= 6/12= 0.5%  

n- Number of months ( n) = 20 × 4 = 48

Annuity factor  

= ( 1- (1.005)^(-48)/0.005= 42.5803

Monthly installment= 20,000 /42.5803  = $469.701

Monthly installment = $469.701

Monthly payment = $469.701

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