Question

your bank will lend you $2,000 for 45 days at a cost of $25 interest. a. what is your annual rate of interest? (use 365 days in a year. do not round intermediate calculations. round the final answer to 2 decimal places.) annual rate of interest % b. what is your effective annual rate? (use 365 days in a year. do not round intermediate calculations. round the final answer to 2 decimal places.) effective annual rate %

Answer 1

The annual rate of interest on a $2,000 loan for 45 days with a cost of $25 interest is approximately 10.15%. Since the loan does not involve compounding, the effective annual rate (EAR) is also 10.15%.

Step-by-step explanation:

When calculating the annual rate of interest, you would take the amount of interest paid ($25), divide it by the principal ($2,000), then divide by the fraction of the year the money was borrowed for (45/365). Multiplying this result by a full year (365 days) gives you the annual interest rate.

To find the annual rate of interest:

Annual rate of interest = (Interest / Principal) / (Days loan is taken/365 days) * 365 days

Annual rate of interest = ($25 / $2,000) / (45/365) * 365 = 0.0125 / (45/365) * 365 ≈ 0.0125 / 0.1233 * 365 ≈ 10.15%

As for the effective annual rate (EAR), it accounts for the effects of compounding over the year. Since the loan is short-term and interest is not compounded in this scenario, the EAR would be the same as the nominal rate given in the question, which is 10.15%.

Effective Annual Rate (EAR) = (1 + (Interest / Principal) / (Days loan is taken/365))^365 - 1

Because the interest is not compounded, the EAR is also 10.15%.