Supposing you are responsible for setting the policy on Effective Annual Rates (

Question

Supposing you are responsible for setting the policy on Effective Annual Rates (EAR) on all loans for a bank in Worcester MA, You have decided that all loans given to people with Credit Score between 500 and 600 should be charged an EAR of 18%. A customer with Credit Score of 540 wants to borrow $200,000 to buy a Condo. The Truth in Lending Act of 1968 AKA Regulation Z requires that cost of borrowing must be quoted in Annual Percentage Rate (APR). According to your calculations, this APR rate is:

Explanation / Answer

We know that EAR = (1+APR/m)^m -1 where m can be 365 for daily APR, 12 for monthly APR & 1 for yearly APR etc. Here we need to find monthly APR for Loan So We have 18% = (1+APR/12)^12 - 1 ie (1+APR/12)^12 = 1+18% = 1.18 Taking Log we get 12Log(1+APR/12) = Log1.18 = 0.0719 ie Log((1+APR/12) = 0.0719/12 = 0.0060 Taking ANti Lo, we get (1+APR/12) = 10^( 0.0060) = 1.0139 ie APR/12 = 0.0139 = 1.39% SO Monthly APR rate is 1.39% Annual APR Rate = 1.39%*12 = 16.67%

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