Financial Mathematics Refincing A woman has an outstanding balance of 180,000 on
ID: 2775593 • Letter: F
Question
Financial Mathematics Refincing
A woman has an outstanding balance of 180,000 on a loan at a nominal interest rate of 5.5% convertible monthly. She has 20 years of monthly payments remaining on her loan, due at the end of each month. She has the opportunity to re-finance at a nominal rate of 4.5% convertible monthly. However, her term will increase to 30 years of monthly payments remaining, and she will have to pay a $3,000 fee to convert. What will her total savings or cost be if she re-finances?Explanation / Answer
Case -1
Monthly rate is 0.055/12 and number of periods is 240 (20*12) and the principla PV = 180,000
She will pay a montly installment of =pmt(0.055/12,240,180000) = 1238.20
Hence she will pay $1,238.20 per month for 240 months and finally she pays 1238.20*240 = $297,167.32
Case -2
Monthly rate is 0.045/12 and number of periods is 360 (30*12) and the principla PV = 180,000
She will pay a montly installment of =pmt(0.045/12,360,180000) = 912.03
Hence she will pay $912.03 per month for 360 months and finally she pays 912.03*360 = $328,332.08
In case two her monthy installment will reduce by $326.17 but since tenure increases she will pay $31,164.76 more on the entire sum and an additonal 3,000 as coversion fee which will make it $34,164.76
Hence the total cost is $34,164.76 and she is advised against the conversion
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