Calculating Loan EAIR from Equal Monthly Payments

Summary

The document compares two ways to interpret the effective annual interest rate on a loan repaid through equal monthly payments. The questioner allocates each payment between principal and interest, divides the estimated monthly interest by the original loan amount, then compounds that rate annually. An answer explains that this treats the loan as if the full original balance remained outstanding throughout repayment, so it does not reflect the declining balance created by monthly principal payments.

The alternative defines EAIR as the annual discount rate that makes the present value of all scheduled payments equal the amount borrowed. It expresses this as a present-value equation and reports a rate of 19.36% for the stated loan terms. The exchange illustrates why loan yield should be inferred from the complete cash-flow schedule rather than a simple interest-to-original-principal ratio. It gives no derivation of the numerical solution or discussion of fees, payment timing conventions, or day-count assumptions, which can matter in practical loan calculations.

Key ideas

• A loan's yield should account for the timing and amount of every payment.
• Dividing a payment's interest component by the original principal ignores the declining loan balance.
• The effective annual rate can be defined as the discount rate that equates payment present value with the amount borrowed.
• The stated calculation reports a 19.36% EAIR for the example loan.

Tags

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


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












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.

## Answer by ZRH (score 2)

https://quant.stackexchange.com/a/44265

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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