GMATCoachBen wrote:
A bank issues a type of loan called a simple discount note, for which a borrower receives from the bank an amount equal to the loan amount minus the simple interest that is charged on the loan amount for the duration of the loan. If the bank issues a simple discount note to a borrower for $25,000 at a simple annual interest rate of 𝑟 percent for 6 months and the borrower receives $24,625 from the bank, what is the value of 𝑟?
A) 2.5
B) 2.75
C) 2.875
D) 3.0
E) 3.125
There is another
Two-Part Analysis one here, which also involves a "discount loan" and people find very confusing (35% correct).
We must make sure to understand the description of this type of loan, and not use our own assumptions of how loans should work. Most of us tend to think of interest being ADDED to the loan amount, such as when we buy a house. However, for this problem, it says:
a borrower receives from the bank an amount equal to the loan amount MINUS the simple interest that is charged on the loan amount for the duration of the loan.So, let's calculate the amount of simple interest (I), using this formula:
Amount Borrower Receives = Loan Amount - I
The loan amount is $25,000, and the borrower receives $24,625.
24,625 = 25,000 - I
I = 375
Next, it's asking for the
"simple annual interest rate of r percent 6 months."Simple Interest formula: I = P\(\frac{r }{ 100}\) T
For the 6 months, T = (6 months / 12 months) = 0.5 years
It's important here to use the correct value for P!
The passage says:
"the simple interest that is charged on the loan amount".So, since the loan amount is 25,000, P = 25,000, not the 24,625.
Now we plug all these values into our formula:
I = 375 = P\(\frac{r }{ 100}\) T = 25,000 * \(\frac{r }{ 100}\) * 0.5
r = \(\frac{375*100 }{ (.5 *25,000)}\) =
3