In this question we will check if a discount is actually a discount. Say you are to borrow $100 for a year at a simple interest rate of 10%. Determine the discount D and the proceeds P for this loan. Next take another look at the situation. You take away P dollars and at the end of the year you pay $100 what rate of simple interest did you actually pay and is this rate more or less than the 10% of the loan with the discount.

I got 110% Can someone help me with this ?

Loan proceeds: Net amount disbursed by a lender to a borrower, under the terms of a loan agreement. from

http://www.businessdictionary.com/definition/loan-proceeds.html
So proceeds,
P = amount disbursed by lender = $100

Discount
= maturity value * rate * time (years)
http://www.ajdesigner.com/php_bank_discounts/bank_discount.php
Discount
D=$110 * 0.10 * 1
=$11

Part B:
P=$100
At the end of the year, you pay back $100.
What is the rate, is this more, or less than 10% ?

If you pay back $100 at the end of the year you didnt pay back any interest it was less than 10% of the loan with the discount

Exactly. In fact, you borrowed $100, you pay back $100, so the interest is ... zero!

To determine the discount (D) and the proceeds (P) for this loan, we need to calculate the interest charged and subtract it from the original loan amount.

The formula for simple interest is: Interest = Principal (P) * Rate (R) * Time (T)

In this case, the principal (P) is $100, the rate (R) is 10% (or 0.10 as a decimal), and the time (T) is 1 year. Plugging in these values, we can calculate the interest:

Interest = $100 * 0.10 * 1 = $10

The discount (D) is the interest charged, which in this case is $10. To find the proceeds (P), we subtract the discount from the original loan amount:

Proceeds (P) = $100 - $10 = $90

So, the discount (D) is $10 and the proceeds (P) are $90.

Next, let's consider the second situation where you take away P dollars and, at the end of the year, repay $100. In this case, the amount you borrowed was P dollars, and you repay $100 after one year.

To determine the rate of simple interest you actually paid, we can use the formula:

Rate (R) = (Interest / Principal) * 100

In this situation, the interest charged is $100 - P (as you repay $100 after deducting P dollars), and the principal is P. Plugging in these values, we can calculate the rate (R):

Rate (R) = [(100 - P) / P] * 100

Let's say you borrowed $90 (which is the proceeds P). Plugging P = $90 into the formula, we get:

Rate (R) = [(100 - 90) / 90] * 100 = (10 / 90) * 100 ≈ 11.11%

Therefore, the rate of simple interest you actually paid is approximately 11.11%.

Comparing this with the original interest rate of 10% for the loan with the discount, we can see that the rate of simple interest you actually paid (11.11%) is more than the 10% of the loan with the discount.

In conclusion, the rate of simple interest you actually paid is 11.11%, which is slightly more than the 10% interest rate on the loan with the discount.