Smithereens
Member
- Joined
- Jan 17, 2007
- Messages
- 255
- Gender
- Male
- HSC
- 2007
Q: A couple borrow $140 000 to buy a house. Interest is charged on the loan at 15% reducible, and the loan (including interest) is to be paid off by equal monthly instalments over 20 years, the first instalment to be made one month ater the time of purchase.
I've worked out the monthly payment to be $1843.51
b) Calculate how much was still owed at the end of 10 years.
My initial working out was this:
The money owed at the end of month 120 (or 10th year):
= 140 000 (1.0125)^120 - M [1.0125^119 + 1.0125^118 + ... + 1]
where M = monthly repayment
Now, substitute the value of M in from the answer you got before ($1843.51):
= 140 000 (1.0125)^120 - (1843.51)[275.21705..... for the sum of the geometric series in the brackets]
= $114 264 is the amt owed at the end of month 120 (or the 10th year)
But my query is, why can't I take the monthly repayment that I first calculated, and multiply by 120 months?
Thanks alot anyone
I've worked out the monthly payment to be $1843.51
b) Calculate how much was still owed at the end of 10 years.
My initial working out was this:
The money owed at the end of month 120 (or 10th year):
= 140 000 (1.0125)^120 - M [1.0125^119 + 1.0125^118 + ... + 1]
where M = monthly repayment
Now, substitute the value of M in from the answer you got before ($1843.51):
= 140 000 (1.0125)^120 - (1843.51)[275.21705..... for the sum of the geometric series in the brackets]
= $114 264 is the amt owed at the end of month 120 (or the 10th year)
But my query is, why can't I take the monthly repayment that I first calculated, and multiply by 120 months?
Thanks alot anyone