Question

scounted Cash Flow Valuation (HW) Problem 6-60 Discount Interest Loans [L04] This question illustrates what is known as discount interest. Imagine you are discussing a loan with a somewhat unscrupulous lender. You want to borrow $24,000 for one year The interest rate is 12 9 percent. You and the lender agree that the interest on the loan will be 129 $24,000 $3,096. So the lender deducts this interest amount from the loan up front and gives you $20,904. In this case, we say that the discount is $3,096. What is the effective annual rate?

Answer 1

The effective annual rate (EAR) for the loan is calculated based on the actual amount received ($20,904) and the total interest paid ($3,096). The EAR comes out to be 14.81%.

Step-by-step explanation:

Calculating the Effective Annual Rate

To calculate the effective annual rate (EAR), we need to consider the terms of the loan as given in the scenario. The lender is offering a loan of $24,000, but they are subtracting the interest of $3,096 up front, effectively giving out only $20,904. To find the EAR, we use the formula for the effective annual rate, which accounts for the actual amount received by the borrower and the total interest paid.

The calculation is as follows:

EAR = (1 + (Interest / Principal Received))^n - 1
Where:
- Interest is the total interest paid over the loan period,
- Principal Received is the actual amount given to the borrower,
- n is the number of compounding periods per year.

In this case, since the loan is for one year and there are no additional compounding periods specified, we will assume n is 1. The calculation is therefore:
EAR = (1 + ($3,096 / $20,904))^1 - 1
EAR = (1 + 0.1481) - 1
EAR = 0.1481 or 14.81%

The effective annual rate of this loan is 14.81%.