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A \$980 loan is paid over 12 months in 12 equal payments of $90 each. What is the loan's EAIR?

980/12=81.666…. (monthly principal payment)

90-81.6666….=8.3333….. (monthly interest payment)

R = 8.33333…../980 = 0.008503=0.8503% (monthly interest rate)

EAIR=[(1+0.008503)^12] -1=0.10695=10.7%

Thanks in advance guys.

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closed as off-topic by LocalVolatility, Helin, skoestlmeier, Lliane, Bram Feb 25 at 15:30

This question appears to be off-topic. The users who voted to close gave this specific reason:

  • "Basic financial questions are off-topic as they are assumed to be common knowledge for those studying or working in the field of quantitative finance." – LocalVolatility, Helin, skoestlmeier, Lliane, Bram
If this question can be reworded to fit the rules in the help center, please edit the question.

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EAIR is the discounting rate, which makes the aggregate Net Present Value (NPV) of 12 90$-payments equal to 980. Therefore, you need to solve the following equation:

$980=\sum_{i=1}^{12}\frac{90}{1+R*i/12}$

where R is the EAIR. I get $R=19.36\%$.

This is commonly referred to as usury :)

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    $\begingroup$ How did you solve your equation? Also, is the equation in your answer basically discounting each $90 payment back to present value? If so, shouldn't there be an exponent in there somewhere? Thanks. $\endgroup$ – user98937 Feb 24 at 21:36
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    $\begingroup$ yes, discounting each payment back. in excel, you can use solver to work it out. no exponent there because by banking convention sub-annual discount factors are written as $1/(1+R*T)$ $\endgroup$ – ZRH Feb 24 at 21:55
  • $\begingroup$ I can see how you did it in Excel (just tried it). Could you direct me to a source for deriving that equation? $\endgroup$ – user98937 Feb 24 at 22:13
  • $\begingroup$ Also, the question didn't specify who the lender was. If the lender was not a bank, how would the equation change? $\endgroup$ – user98937 Feb 24 at 23:04
  • $\begingroup$ Shouldn't it be $980=\sum_{i=1}^{12}\frac{90}{(1+R/12)^i}$ ? That gives 18.329% $\endgroup$ – Alex C Feb 25 at 0:56

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