Rate for borrowers with high interest rate is calculated with the given formula when effective interest rate is given:
R = [(1 + r ) ( 1 + s) -1] or = (r + s + r*s)
where R = Rate of interest with default risk = 30%
r = Rate of interest without default risk = 15%
s = Difference between default interest rate and without default interest rate ( Compensation for Default risk ) =
(30-15) = 15%
R = (1 + .15) (1 + .15) - 1 or (.15 + .15 + .15*.15)
= 32.25%
where r*s = (.15*.15) = 2.25%
Hence the error involve in the decomposition of interest rate with higher default of risk is 2.25% i.e.( 32.25% - 30%)
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