A George has just emailed me, asking about another General Mathematic question, this time from 2025 NHT Exam 1. The question and the exam report comments are below, and I haven’t looked at all. Again, treat this post as a proto-WitCH.* George (or I) can add more context once people have given their thoughts, and if it seems there is an issue.
*) Guys, I’m always happy to look at and/or post on questionable questions, but it is preferable to not ask me the day before the exam …
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Sorry George – I don’t see the issue here, please give some more context.
The unknown is the loan term, but since the payments are given, you assume this will pay off the loan completely and then solve for N (number of payments). The Finance Solver (on the TI CAS), I assume Casio has a similar function, then gives 10 years at 4 payments per year, so 40 payment periods.
Half-way through the loan then means 20 of these and, again using the finance solver you can work out the balance owing after 20 payments.
Unless I have missed something (it happens a lot) I think this question is fairly standard for VCAA.
Hi there!
My concern (probably more an error in my conceptual understanding) is regarding the answer that VCAA had posted. To find the total payment made, why would it suffice to just add the remaining balance after 20 payments? Why should we not account for any interest on the final balance? Is it because we just need the balance to go to 0?
If I knew that the 20th payment was my final payment, I personally would’ve found the balance of the loan after 19 payments and find the PMT for 1 final payment.
In previous VCAA questions, they tend to specify whether it’s a final repayment question or a lump sum question. In a separate scenario, let’s say that Kenneth made 20 repayments and the final repayment was different from the regular scheduled payment. Why would we, in this scenario, find the balance after 20 payments and add/subtract from the regular payment? I wouldn’t be able to just do (regular payment * n) + FV (like how they’ve done in their working out).
Again, it could be a conceptual misunderstanding I might be overthinking, but I do appreciate the feedback.
Geez, you guys. You’re supposed to be helping, not just leeching. Is George correct or not?
George, the way I read the sentence “Halfway through the term of the loan, Kenneth pays off the entire remaining balance in one payment” is that immediately after Kenneth makes his regularly scheduled 20th payment, he pays off the remaining balance with one lump sum. So no additional interest is accrued on the remaining balance.
I think in your alternative scenario, VCAA’s method is still correct. Let’s keep the same principal and interest rate compounding quarterly, but now suppose Kenneth is scheduled to make 20 payments of 9610.50 each quarter. After 20 equal payments, Kenneth still owes 1.07, and so he just adjusts his final payment by adding this on to the regular payment amount – no interest is accrued on this 1.07. So the total amount he would pay for the loan is 20 * 9610.5 + 1.07.
(In effect, the typical “what’s the final repayment amount?” question is asking for what lump sum payment is needed to balance the ledger, after the scheduled number of regular equal payments).
Thanks, SRK.
I also don’t see an issue with this one but I see how it could be misunderstood. In what I have seen to differentiate these questions would be if the ‘final payment’ is considered in the question. If it’s not mentioned it would be just assuming I=(pmt * N) -change in balance. Did the term of the regular loan (without the extra payment) N value round out with multiple decimals to 40 exactly? In that case as well, considering the final payment wouldn’t have made a significant difference.
Thanks, B.