# This question illustrates what is known as discount interest. Imagine you are discussing a loan...

## Question:

This question illustrates what is known as discount interest. Imagine you are discussing a loan with a somewhat unscrupulous lender. You want to borrow $27,000 for one year. The interest rate is 13.2 percent. You and the lender agree that the interest on the loan will be .132 x 27,000 = $3,564. So the lender deducts this interest amount from the loan up front and gives you $23,436. In this case, we say that the discount is $3,564.

What is the effective interest rate? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

## Discount Interest

In discount interest, the interest due is paid at once, at the beginning of the loan. The interest payment is deducted from the original loan amount. This means that you will get a smaller loan amount (net of interest).

For Example:

If you want to borrow $10,000 at a rate of 10%. The interest payment for this loan is $1,000 ($10,000 x 10%). In discount interest, this amount is paid upfront and deducted from the loan amount. This means that you will only get $9,000 ($10,000 - $1,000). This has the effect of changing the interest rate on the loan.

At the beginning the stated interest rate is 10%. However, the effective interest rate of the loan is 11.11%. This is calculated by:

{eq}\frac{1,000}{9,000} = 0.1111 {/eq}

## Answer and Explanation:

#### What is the effective interest rate? (Do not round intermediate calculations.)

At a interest rate of 13.2%, the interest on a $27,000 loan is...

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#### Learn more about this topic:

from NY Regents Exam - Integrated Algebra: Help and Review

Chapter 16 / Lesson 7