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March 29, 2024, 05:04:40 am

Author Topic: Total cost of a Loan  (Read 1659 times)  Share 

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sam777

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Total cost of a Loan
« on: February 21, 2022, 08:20:26 pm »
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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

Golgi Apparatus

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Re: Total cost of a Loan
« Reply #1 on: February 22, 2022, 02:23:57 pm »
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When you’re repaying a loan, you cannot have a non-integer number of payments. Either you make a payment or you don’t, so the number of payments must be a whole number. N is not the amount of full payments you make (which could be a decimal), it is the number of times you go to  the bank and give them money, which must be an integer. Even if you pay 14 full payments then a final smaller payment, you still have to go to the bank 15 times, so you are still making 15 payments. You cannot go to the bank 14.89 times.

The value of N doesn’t change depending on the size of the payments - it has to be a whole number. This is why you change N to 1 - you are calculating how much you have to pay to make the future value 0 by making one more payment. You can’t make 0.89 payments.

I hope this makes sense!
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