A buyer is getting a fully amortized loan for $220,000. The bank will give the buyer the loan for 15 years at 5 1/2% or for 30 years at 6 1/2%. To the nearest dollar, what is the difference between the monthly payments for these two loans?

Difference in monthly payment=$407.0339

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 installment is computed as follows:  

Monthly installment= Loan amount/annuity factor

Loan amount; =220,000

Annuity factor = (1 - (1+r)^(-n))/r

r -monthly rate of interest, n- number of months

First option

monthly interest rate = 5.5% =0.458 %, n- 15×12

Annuity factor= (1-(1+0.055)^(-180 )/0.055 =122.38

Monthly repayment = 220,000/122.386 = 1797.58

Second option

r- 6.5%/12 = 0.542  % n = 15×12 = 180

Annuity factor = ( 1- (1+0.00542)^(-360))/0.005 42= 158.21

Monthly installment = 220,000/1390.549  = 1390.54

Difference in monthly payment = 1,797.583 -  1390.54 =  407.0339

Difference in monthly payment=407.0339

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