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Andru [333]
3 years ago
9

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 y

ears at 6 1/2%. To the nearest dollar, what is the difference between the monthly payments for these two loans?
Business
1 answer:
Vadim26 [7]3 years ago
6 0

Answer:

Difference in monthly payment=$407.0339

Explanation:

<em>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. </em>

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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