Patty wants to buy a home with a cash price of $750,000. The bank requires 20% d
ID: 2756139 • Letter: P
Question
Patty wants to buy a home with a cash price of $750,000. The bank requires 20% down payment and charges 4.5% (12) and 1.5 points for a 30 year mortgage. Find the size of Patty’s monthly payments (round up to the nearest cent). After 10 years, Patty has the option of refinancing to a rate of 3% (12) with the bank charging 1 point. Patty declines, but 10 years later (20 years from the start of the mortgage), she decides to refinance at 3.5% (12) with no points. How much did the refinancing save her compared to the original mortgage? Was the earlier refinancing offer better than the one she took (assuming she could only refinance one)?
Explanation / Answer
Purchase Price = 750000
Down Payment = 20%*750000 = 150000
Loan Required = 600000
1.5 point is the upfront cost
Loan to be taken = Loan Required /(1-upfront cost)
Loan to be taken = 600000/(1-1.5%)
Loan to be taken = 609,137.06
Monthly rate =4.5/12 = 0.375%
no of month = 30*12 = 360
Patty’s monthly payments = Loan to be taken/((1-(1+r)^-n)/r)
Patty’s monthly payments = 609137.06/((1-(1+0.375%)^-360)/(0.375%)
Patty’s monthly payments = 3086.41
After refinance at year 20
Amount outstanding = monthly payments *(1-(1+r)^-n)/r
Amount outstanding = 3086.41*(1-(1+0.375%)^-120)/0.375%
Amount outstanding = 297,805.61
After Refinance
Monthly Payment = Amount outstanding / ((1-(1+r)^-n)/r)
Monthly Payment = 297,805.61/(((1-(1+(3.5%/12))^-120)/(3.5%/12))
Monthly Payment = 2944.88
From refinancing
Total Amount Saved = Reduction in Monthly Payment * No of month
Total Amount Saved = (3086.41-2944.88)*120
Total Amount Saved = $ 16,983.60
If it has refinanced at year 10
Amount outstanding = monthly payments *(1-(1+r)^-n)/r
Amount outstanding = 3086.41*(1-(1+0.375%)^-240)/0.375%
Amount outstanding = 487854.74
Loan amount required for refinancing = Amount outstanding /(1-upfront cost)
Loan amount required for refinancing = 487854.74/(1-1%)
Loan amount required for refinancing = 492,782.57
After Refinance
Monthly Payment = Amount outstanding / ((1-(1+r)^-n)/r)
Monthly Payment = 492,782.57/(((1-(1+(3%/12))^-240)/(3%/12))
Monthly Payment = 2732.96
Total Saving if it has refinaced at year 10 = (3086.41-2732.96)*240
Total Saving if it has refinaced at year 10 = $ 84,828
Yes the earlier refinancing offer better than the one she took
Answer
Patty’s monthly payments = 3086.41
Total Amount Saved from refinancing at year 20= $ 16,983.60
Yes the earlier refinancing offer better than the one she took