Question

An individual is borrowing $165,000 for a 25 year loan at 4.0% per year compounded monthly. Compute the monthly payment. Immediately after his 108th monthly payment he decides to refinance at a lower rate of 3% per year compounded monthly for 100 monthly payments. What would be his new monthly payment and how much interest will he save? Draw the cash flow diagrams.

Please show your work with the formula you use to solve this problem. Thanks!

Answer 1

Loan amount = 165000

t = 25 yrs = 25 * 12 = 300 months

i = 4% = 4% / 12 = 0.3333% per month

(A/P, i%,n) = i*((1 + i)^n)/((1 + i)^n-1)

(P/A, i%,n) = ((1 + i)^n-1)/(i*(1 + i)^n)

Monthly payment = 165000 * (A/P, 0.3333%,300)

= 165000 * 0.003333* ((1 + 0.003333)^300)/((1 + 0.003333)^300 - 1)

= 165000 * 0.003333* ((1.003333)^300)/((1.003333)^300 - 1)

= 165000 * 0.005278

= 870.89

Loan installments left after 108 payments = 300 - 108 = 192

Loan amount due = 870.89 *(P/A, 0.3333%,192)

= 870.89 * ((1 + 0.003333)^192 - 1)/(0.003333*(1 + 0.003333)^192)

= 870.89 * ((1.003333)^192 - 1)/(0.003333*(1.003333)^192)

= 870.89 * 141.647887

= 123360.34

New interest rate = 3% = 3% / 12 = 0.25% per month

new loan tenure = 100 months

New monthly installments = 123360.34 * (A/P, 0.25%,100)

= 123360.34 * 0.0025* ((1 + 0.0025)^100)/((1 + 0.0025)^100 - 1)

= 123360.34 * 0.0025* ((1.0025)^100)/((1.0025)^100 - 1)

= 123360.34 * 0.011314

= 1395.75

Interest paid in first case over life of loan =  870.89 * 300 - 165000 = 96267

Interest paid in second case = 870.89 * 108 + 1395.75 * 100 - 165000 = 68631.12

Interest saved = 96267 - 68631.12 = 27635.88

CFD