Question

a lender charges an effective per annum interest rate of

I) 15% to group of borrowers with no default risk

ii)30% to a group of borrowers with very high default risk

determined the error involved in decomposing the rate for borrowers with high default risk into the sum of the rate for borrowers with no default risk and the rate that compensate for default risk,

I.e the error involved in ignoring the rs term

Need step by step solution please thanks

Answer 1

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%)