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rani recently took out a $50,000 secured line of credit. The rate is 2.75% compounded semi- annually above the bank of canada rate which is currently 1%. 

If rani could afford to make payments of $700 per month, how long would it take her to pay of the outstanding balance on her line of credit? 

( use a graphing calculator or your brain) 

B) How much total interest would she pay? 

C) How many fewer payments and less interest would she have to pay if she was able to make monthly payments of $1200?

Guest Oct 13, 2017
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Rani's interest rate would be: 2.75 + 1 =3.75% compounded semi-annually.

You have to convert the above rate to compounded monthly =3.72103442307%

Then you have to use this formula to calculate the monthly payment or the number of months needed to pay off the loan: PMT=PV. R.{[1 + R]^N/ [1 + R]^N - 1}

 

Unfortunately, there is no direct method of finding the number of months, N, to pay off the line of credit @ $700 per month.  See the note below. However, if you have a financial calculator and you enter all the known variables and solve for N, you should get N =80.87 or ~81 months.

Total interest would be: [80.87  x  $700]  -  $50,000 =$6,609.00...........(1)

 

If she could afford to pay $1,200 per month, then it would take, N=44.68 months.

Total interest would be:[44.68  x  $1,200]  -  $50,000 =$3,616.00............(2)

 

Just subtract (2) from (1) above to get the difference in interest that she would save.

 

Note: There is a relatively involved formula for finding N, or the number of months and it looks like this:  N =Log[(-FV*R+PMT) /(R*PV+PMT)] / Log[R+1]

Guest Oct 13, 2017
edited by Guest  Oct 13, 2017

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