Hi,
So as we know, the total cost of a reducing balance loan can be determined by multiplying the number of payments with the amount per payment.
Here's the catch though. According to every single one of my school's further teachers, if the number of payments is not a whole number (e.g. 14.89), then you cannot just multiply that non-integer number with the payment amount to find the total cost of the loan (or the total amount you have lost in taking out the loan)
Instead, you must multiply the number of whole payments (14 in that example) with the payment amount to first find the remaining money owed (FV) after all the whole equal payments.
Then, you must use that value and calculate the interest and final payment for one more period. To do this, you let FV equal PV, N=1 (here's my first question: Why do you let N=1 still and not 0.89 for the above example) and FV=0. Solve for PMT which should give you the final payment amount.
This final payment amount should be added to the total cost of all the whole equal payments that you initially solved for (14XPMT). Then this answer is your total cost of the loan.
My second question: Why can't you just use the non-integer number and multiply it to the PMT amount to find the total cost? Why do you have to split it into equal whole payments cost and final fractional payment cost.
Would appreciate if anyone who knows can reply.
Thx