You are in the market for a mortgage loan. You are contemplating a 15 or 30 year
ID: 2707438 • Letter: Y
Question
You are in the market for a mortgage loan. You are contemplating a 15 or 30 year mortgage. The loan officer states, "Thousands of dollars can be saved by switching to a 15-year mortgage from a 30-year mortgage." Is the loan officer correct? The 30-year mortgage has a 9% interest rate versus a 15-year mortgage with 8.5% interest. Both mortgages are for $100,000 and have monthly payments.
Explanation / Answer
Hi,
Please find the answer as follows:
You need to calculate the future value of both the options to derive the answer.
Option A:
Rate = 8.5%/12
Nper = 15*12 = 180
PV = 100000
PMT = 0
FV = ?
Future Value = FV(Rate,Nper,PMT,PV) = FV(8.5%/12, 180,-100000,0) = 36178635.32
Option B:
Rate = 9%/12
Nper = 30*12 = 360
PV = 100000
PMT = 0
FV = ?
Future Value = FV(Rate,Nper,PMT,PV) = FV(9%/12, 360,-100000,0) = 183074348.31
Net Outflow = Option B - Option A = 183074348.31 - 36178635.32 = 146895713
Option A results in a lesser outlow by 146895713. Therefore, the loan officer is correct.
Thanks
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