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Problem 21-11 Prepayments (1
Problem 21-11 Prepayments (1.03, CFA1)
Consider a 30-year, $155,000 mortgage with a rate of 6.05 percent Ten years into the mortgage, rates have fallen to 5 percent. What would be the monthly saving to a homeowner from refinancing the outstanding mortgage balance at the lower rate? (Do not round Intermediate calculations. Round your answer to 2 decimal places.)
Expert Solution
First we calculate Monthly Payment using PMT Function in Excel:
=pmt(rate,nper,-pv,fv)
Here,
PMT = Monthly Payment = ?
Rate = 6.05%/12 = 0.5042% compounded monthly
Nper = 30 years*12 months = 360 months
PV = $155,000
FV = 0
Substituting the values in formula:
=pmt(0.5042%,360,-155000,0)
PMT or Monthly Payment = $934.29
Now, We calculate Future Value at the End of 10 Years using FV Function in Excel:
=fv(rate,nper,pmt,-pv)
Here,
FV = Future Value = ?
Rate = 6.05%/12 = 0.5042% compounded monthly
Nper = 30 years*12 months = 360 months
PMT = Monthly Payment = $934.29
PV = $155,000
Substituting the values in formula:
=fv(0.5042%,360,-934.29,-155000)
FV or Future Value = $129,885.67
At last we calculate Monthly Payment when interest rate falls to 5% using PMT Function in Excel:
=pmt(rate,nper,-pv,fv)
Here,
PMT = Monthly Payment = ?
Rate = 5%/12 = 0.4167% compounded monthly
Nper = 20 years*12 months = 240 months
PV = $129,885.67
FV = 0
Substituting the values in formula:
=pmt(0.4167%,240,-129885.67,0)
PMT or Monthly Payment = $857.19
Monthly Savings = $934.29-$857.19 = $77.10
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