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Question 1115298: "Question 16
Sam plans to buy a car for R125 000. He pays a 15% deposit and manages to secure a bank loan for the outstanding amount. The bank charges 12,5% per annum, compounded monthly. Determine what Sam’s
minimum monthly payment will be if the loan has to be repaid in six years’ time.
[1] R998,17
[2] R2 104,94
[3] R2 476,40
[4] R1 476,69
the car costs 125,000
the deposit is 15% of 125,000 = 18,750
the amount of the loan is 125,000 - 18,750 = 106,250
the bank charges 12.5% per year compounded monthly.
12.5 per year compounded monthly equals 12.5/12 = 1.0416666667% per month.
the loan needs to be repaid in 6 years.
6 years * 12 months per year would be 72 months.
using the texas instruments BA II financial calculator, you would make the following entries.
PV = 106,250
FV = 0
I/Y = 12.5 / 12 = 1.041666666...
N = 12 * 6 = 72
you would then calculate PMT to get:
PMT = -2,104.937737
that's a monthly payment of 2,104.94, which is selection 2. "
Consider the amortisation of Sam's loan in question 16 above. Suppose Sam pays all minimum monthly payments on time into this loan account. In which month will the principal that is paid off in the month for the time be more than the interest paid off?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! i'm not exactly sure how to answer that last one.
you're correct up to the last part.
you want to know the month in which the principal that is paid off is greater than the interest paid off in that month.
there may be an easier way to do it, but i'll have to do it the hard way until i figure it out.
i used excel and determined that the interest is less than half of the payment in the 7th month.
that was the easy way, assuming you know how to calculate the month by month payments and interest and principal.
using just logic, i determined the following:
the payments every month are the same.
the interest is taken off the remaining balance from the previous month and then the payment is made.
if the payment is 2104.937737, and you want the interest to be half of that payment, then you would divide the payment by 2 to get 1052.468869.
in order for the interest to be 1052.468869, the principal would have to be that divided by (.125/12).
that becomes 1052.468869 / .010416667 which makes the remaining balance equal to 101,037.0114.
you can solve for the number of months it would take to pay that off.
you would keep i/y the same and pmt the same.
you would set fv = 0 (it should already be).
you would keep payments at the end of the month (they should already be so)
you would replace pv with -101,037.0114.
you would solve for n to get 66.88810435 months.
subtract that from the original term of 72 months, and you get 5.111895653 months.
what this formula says is that the remaining balance would be equal to 101,037.0114 at the end of 5.111895653 months.
what that says is:
at the end of the 5th month, the remaining balance is greater than that.
at the end of the 6th month, the remaining balance is less than that.
since the interest is calculated from the remaining balance of the previous month, then you would expect the interest to be less than half the payment in the 7th month.
the excel printout confirms that.
i used excel because i have it and i know how to use it.
without excel, you could use the ti-ba-ii to tell you the interest and the principal.
you can use the ti-ba-ii to find out the remaining balance and the interest and the principal.
after you've solved for the payment, then enter 2d pv, which bring up the amort schedule.
you will be prompted for p1.
enter 6 and then hit the enter key.
hit the down arrow.
you will be prompted for p2.
enter 6 and then hiT the enter key.
hit the down arrow.
it tells you the balance is 100,102.8518
hit the down arrow again.
it tells you the principal part of your payment is 1051.249185
hit the down arrow again.
it tells you the interest part of your payment is 1053.688552.
***** the principal part of your payment is NOT greater than the interest part of your payment.
hit 2d pv again.
you will be prompted for p1.
enter 7 and then hit the enter key.
hit the down arrow.
you will be prompted for p2.
enter 7 and then hit the enter key.
hit the down arrow.
it tells you the balance is 99,040.65215.
hit the down arrow again.
it tells you the principal part of your payment is 1062.199697
hit the down arrow again.
it tells you the interest part of your payment is 1042.73804
***** the principal part of your payment IS greater than the interest part of your payment.
the transition happened between the 6th and 7th month.
here's a display of the excel spreadsheet that tells you the same thing.
if you do the ti-ba-ii thing, then your remaining balance in the 6th and 7th month and your interest in the 6th and 7th month and your principal in the 6th and 7th month should agree with what the excel printout is telling you.
first few months.
last few months.
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