Quoting from "Numbers Guide" book by The Economist (sixth edition):
"An even bigger discrepancy occurs with discounting of interest on many personal or consumer loans. For example, an advance of $1,000 at 12.5% discounted in advance and repayable over 12 months attracts interest of $125. The principal is grossed up and repaid in installments of $1,125 ÷ 12 = $93.75. But since the balance declines steadily the effective interest rate is actually 24.75%. This is nearly double the quoted discount rate"
Could somebody explain how the 24.75% eip is being calculated?
The closest I could get to that number is with the Python code below but the calculations don't make sense to me.
def eir(i, PV, n): return (i / PV) / n pv = 1000 r = 0.125 fv = pv * (1 + r) installment = fv / 12 rs = 0 f = 1 print(pv, fv, installment) while fv > 0: r = eir(installment, fv, 1) print(r) rs += r fv -= installment print('result=', rs/12)
Which gives about 25.86%.