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I'm trying to figure out the fee-adjusted interest rate paid when incurring a balance transfer fee on a loan, not accounting for inflation.

If the APR is 4%, the loan 5000, the transfer 2% and you pay it off in 200 days (54.8% of the year when rounded to 2 decimals), I see it this way:
(APR: 4% Loan: 5,000 Transfer fee: 2% Days: 200)

Present Value: 4,900 (Loan - transfer fee %)
Future Value: 5,109.589041095890411 (loan * ( APR * (200/365) ) )
Real Rate Over 200 Days: 4.2773273693039% ( (FV - PV) / PV )
Real Rate Over 365 days: 7.806122448979618% ( ( (FV - PV) / PV ) * (365/200) )

Is there something missing and if so, what?

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If real does not mean adjusted for inflation, does it just mean including fee? Also 200 is not 5.48% of the year. –  Henry Mar 17 '11 at 19:09
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1 Answer

up vote 1 down vote accepted

I would expect the amount to be paid after 200 days to be $$5000 \times 1.04^{200/365} \approx 5108.617$$ so the effective interest rate including fees over 200 days to be $$\frac{5108.617}{5000\times 0.98}-1 \approx 4.2575\%$$ and the annualised effective interest rate including fees to be $$\left(\frac{5108.617}{5000\times 0.98}\right)^{365/200}-1 \approx 7.9060\%$$ and these numbers are close to but not the same as yours.

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