# Effective Annual Interest Rate (EAIR) in a 12-month loan [closed]

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%

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

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• "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
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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 :) • 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. – user98937 Feb 24 at 21:36
• 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 $1/(1+R*T)$ – ZRH Feb 24 at 21:55
• Shouldn't it be $980=\sum_{i=1}^{12}\frac{90}{(1+R/12)^i}$ ? That gives 18.329% – Alex C Feb 25 at 0:56