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Homework answers / question archive / You decide to take a 30-year mortgage of $160,000 offered by the Bank of Montreal

You decide to take a 30-year mortgage of $160,000 offered by the Bank of Montreal

Finance

You decide to take a 30-year mortgage of $160,000 offered by the Bank of Montreal. Instead of making the monthly payment of $918.91 every month, you can make half the payment every two weeks (so that you will make 52 ÷ 2 = 26 payments a year). How long will it take to pay off the mortgage if the EAR on the loan is 5.75%? (Note: Be careful not to round any intermediate steps less than six decimal places.) 
The amount of time to pay off the loan is 
weeks. (Round to the nearest integer.) 
 

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Computation of Number of Weeks it will take to pay off the mortgage:

Biweekly Payment = $918.91*1/2 = $459.455

Biweekly Interest rate = (1+5.75%)^(1/26)-1

Biweekly Interest rate = 0.215261%

No of Biweekly Periods = nper(rate,pmt,pv,fv)

No of Biweekly Periods = nper(0.215261%,459.455,-160000,0)

No of Biweekly Periods = 643.99 or 644

No of year it will take to pay off the mortgage = No. of Biweekly / Biweekly in a year

No of year it will take to pay off the mortgage = 644/26

No. of year it will take to pay off the mortgage = 24.77 Years

Number of Weeks it will take to pay off the mortgage = 24.77*52 = 1,287.99 weeks or 1,288 weeks

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