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Question 1167447: You can afford a $200 per month car payment. You've found a 5 year loan at 2% interest. How big of a loan can you afford?
Found 2 solutions by Theo, ikleyn:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! you can afford monthly payments at the end of each month of 200 dollars.
the loan is for 5 years.
the interest rate is 2%.
you can use a formula to solve this, or you can use a financial calculator.
i prefer the use of a financial calculator.
there is one online that you can use.
it can be found at https://arachnoid.com/finance/index.html
here's what the inputs look like:
here's what the output looks like.
your solution is that the amount of the loan you can afford is 11,410.47.
Answer by ikleyn(52800)  (Show Source):
You can put this solution on YOUR website! .
You can afford a $200 per month car payment. You've found a 5 year loan at 2% interest.
How big of a loan can you afford?
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This my solution goes second after the solution by @Theo.
@Theo used an online calculator in his solution.
Since this web-site is to teach Math, the expected solution should be mathematical.
So, I present here a standard mathematical solution.
Calculator can be used as a secondary tool for verification.
Then the sequence of steps would be normally educative.
Use the standard formula for the monthly payment for a loan
M = 
where L is the loan amount; r =  is the effective interest rate per month;
n is the number of payments (same as the number of months); M is the monthly payment.
From this formula, the expression for the maximum loan is
L =  .
In this problem M = $200; r = , n = 5*12 = 60 monthly payments.
Substitute these values into the formula and get for the maximum loan amount
L =  = $11,410.47.
ANSWER. The maximum loan amount is $11,410.47.
Solved.
Compare my answer with the answer by @Theo: they coincide "cent-to-cent".
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In such calculations, it is important to avoid intermediate rounding.
Rounding can be done at the end, only.
Intermediate rounding is PROHIBITED, since it leads to wrong answer.
Also, a calculator should provide the necessary precision.
I use MS Excel in my computer. It works with 15 decimals in mantissa
and provides the necessary precision.
I simply copy-paste my numerical formula into Excel spreadsheet and get the answer in one click.
Many standard online calculators provide the necessary precision.
You may use, for example, these free-of-charge online calculators
https://www.omnicalculator.com/finance/annuity-future-value
https://www.calculatorsoup.com/calculators/financial/future-value-annuity-calculator.php
https://www.calculator.net/future-value-calculator.html
They are reliable, have convenient user-friendly interface, have complete instructions and descriptions,
provide the necessary precision and were checked million times. You may use them to check my/your calculations.
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- - - - - added for your better understanding - - - - -
Notice that the full outpayment in 5 years in this problem is 5*12*200 = 12000 dollars.
It does not contradict to my answer, since the outpayment for the loan ($12000 in this case)
is always greater than the loaned amount ($11,410.47).
The difference is what the financial company earns on this loan.
//////////////// INTERESTING and useful to know ////////////////
If you request an AI with this assignment, there is non-zero probability
that the AI will produce incorrect answer.
For example, today, Oct.1, 2025, I submitted this problem to the Google AI called "Overview".
It produced incorrect answer "A loan of approximately $11,302.28. can be afforded. "
Compare with my correct answer $11,410.47.
At the end of their solution, they say that their value is approximate, so this excuses them.
But in banking calculations and in solving school problems, where the answer should match precisely,
such a discrepancy is  .
This discrepancy is a consequence of the fact that their calculation procedure is DEFECTIVE.
I observed similar discrepancy in many their solved problems in Finance
(more than in 10 cases and more than in 20), so it happens REGULARLY.
Many times I pointed them to this their deficiency, but it looks like
they do not understand the problem - so they still did not fix it,  .
X X X X X X X X X X X X X X X X X X X X X
Come again to this forum soon to learn something new
or to get a precise solution in the future,
with complete and comprehensive explanations.
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