Determining Interest Rate Based On Certain Variables

[JoeA]

Ok, so I am trying to figure out whether or not I can determine the interest rate for an auto loan based on the following parameters:

Total Original Loan Amount: 21428.0

Current Loan Amount: 19662.0

Monthly Payment: 606

Number Of Payments To Date: 12 - Meaning the number of payments that were made up until now

Total Amount Paid To Date: 606 * 12 = 7,272

Any help with this would be greatly appreciated. Thanks.

 

[BigBeachBanana]

Ok, so I am trying to figure out whether or not I can determine the interest rate for an auto loan based on the following parameters:

Total Original Loan Amount: 21428.0

Current Loan Amount: 19662.0

Monthly Payment: 606

Number Of Payments To Date: 12 - Meaning the number of payments that were made up until now

Total Amount Paid To Date: 606 * 12 = 7,272

Any help with this would be greatly appreciated. Thanks.

Is it a homework question or a personal question? Depending on your answer, you'll get different responses.
Also, if you know the term of the loan, it'll simplify the problem, but not necessary.

 

[JoeA]

Is it a homework question or a personal question? Depending on your answer, you'll get different responses.
Also, if you know the term of the loan, it'll simplify the problem, but not necessary.

It's more personal than anything. Its something that a friend asked me a couple of days ago (he's creating a loan calculator app that calculates based on different variables and one of them is with no term) and it's been stuck in my head ever since. So much so that it lead me here LMAO. Thanks for your reply. Let me know if theres anything else I can help you with.

 

[BigBeachBanana]

Yes, it's possible to find the interest rate and the term loan given the information.
Let [imath]n[/imath] be the term of the loan (in months), [imath]m[/imath] be the remainder of the loan term. Since 12 payments have been made, we have [imath]m+12=n\\[/imath]
Let [imath]i[/imath] be the monthly effective interest rate. Assuming the payments are due at the end of the month.
[math] 21428=606\left(\frac{1-(1+i)^{-n}}{i}\right)\\ 19662=606\left(\frac{1-(1+i)^{-(n-12)}}{i}\right) [/math]System of two equations and two unknowns.
[math]\implies i=2.22208\%, n=70.0947 \text{ months}[/math]If you want the nominal annual rate, or the APR, then [imath]r=2.22208\%\times 12 = 26.665\%[/imath].

 

[Deleted member 4993]

Ok, so I am trying to figure out whether or not I can determine the interest rate for an auto loan based on the following parameters:

Total Original Loan Amount: 21428.0

Current Loan Amount: 19662.0

Monthly Payment: 606

Number Of Payments To Date: 12 - Meaning the number of payments that were made up until now

Total Amount Paid To Date: 606 * 12 = 7,272

Any help with this would be greatly appreciated. Thanks.

Any penalty accrued due to late payment?

 

[JoeA]

Any penalty accrued due to late payment?

Let's assume no.

Also I believe @BigBeachBanan gave the correct equation.

 

[JoeA]

Yes, it's possible to find the interest rate and the term loan given the information.
Let [imath]n[/imath] be the term of the loan (in months), [imath]m[/imath] be the remainder of the loan term. Since 12 payments have been made, we have [imath]m+12=n\\[/imath]
Let [imath]i[/imath] be the monthly effective interest rate. Assuming the payments are due at the end of the month.
[math] 21428=606\left(\frac{1-(1+i)^{-n}}{i}\right)\\ 19662=606\left(\frac{1-(1+i)^{-(n-12)}}{i}\right) [/math]System of two equations and two unknowns.
[math]\implies i=2.22208\%, n=70.0947 \text{ months}[/math]If you want the nominal annual rate, or the APR, then [imath]r=2.22208\%\times 12 = 26.665\%[/imath].

Dude, Thank You. You literally saved my sanity!!!

 

[jonah2.0]

Beer induced ramblings follows.

[math] 21428=606\left(\frac{1-(1+i)^{-n}}{i}\right)\\ 19662=606\left(\frac{1-(1+i)^{-(n-12)}}{i}\right) [/math]System of two equations and two unknowns.
[math]\implies i=2.22208\%, n=70.0947 \text{ months}[/math]If you want the nominal annual rate, or the APR, then [imath]r=2.22208\%\times 12 = 26.665\%[/imath].

Did the same system of two equations and two unknowns with the TI89 emulator app and I get a "false" error message. Thought maybe that was my phone acting up due to low storage.
Same deal with Desmos though.

JoeA Determining Interest Rate Based On Certain Variables

www.desmos.com

WA keeps giving me "Standard computation time exceeded..."

21428=606(1-(1+x)^(-y))/x, 19662=606(1-(1+x)^(-(y-12)))/x - Wolfram|Alpha

Wolfram|Alpha brings expert-level knowledge and capabilities to the broadest possible range of people—spanning all professions and education levels.

www.wolframalpha.com

What am I missing?

 

[BigBeachBanana]

Beer induced ramblings follows.

Did the same system of two equations and two unknowns with the TI89 emulator app and I get a "false" error message.
Same deal with Desmos.

JoeA Determining Interest Rate Based On Certain Variables

www.desmos.com

WA keeps giving me "Standard computation time exceeded..."

21428=606(1-(1+x)^(-y))/x, 19662=606(1-(1+x)^(-(y-12)))/x - Wolfram|Alpha

Wolfram|Alpha brings expert-level knowledge and capabilities to the broadest possible range of people—spanning all professions and education levels.

www.wolframalpha.com

What am I missing?

Not sure, but I used WA's system of equations solver:

system of two equations - Wolfram|Alpha

Wolfram|Alpha brings expert-level knowledge and capabilities to the broadest possible range of people—spanning all professions and education levels.

www.wolframalpha.com

 

[Deleted member 4993]

Those equations and two unknowns cannot be solved in elementary algebraic manner. You will need to invoke Mr. Newton's ghost.