Math Problem Statement

Payday loans​ (also called cash advance​ loans) are​ short-term, high-interest loans marketed as a way for people to borrow money for a short period of time until their paycheck arrives.​ However, like many other​ short-term loans, they should be used with extreme caution. Payday loans typically carry a fixed fee of​ $15 to​ $30 per​ $100 borrowed, and lenders sometimes demand access to your checking account to make sure you will pay the fees. Complete parts​ (a) through​ (c) below. Question content area bottom Part 1 a. Consider a payday loan that has a fixed fee of ​$16 per​ $100 borrowed that is due in 2 weeks​ (when your paycheck​ arrives). If you borrow ​$300​, what is the total fee​ (not including your ​$300 ​principal) you owe the lender at the end of 2​ weeks? ​$    enter your response here ​(Round to the nearest cent as​ needed.) Part 2 b. What is the interest rate for that​ 2-week period?    enter your response here​% ​(Round to the nearest whole number as​ needed.) Part 3 c. What is the equivalent annual percentage rate​ (APR) for this​ loan? (Assume that there are 52 weeks in 1​ year). How does this rate compare to other common types of​ loans, such as credit cards or​ mortgages? The​ pay-day loan has an APR of    enter your response here​%. This is ▼ comparable much lower a little lower much higher a little higher than other common types of loans. ​(Type an integer or a​ decimal.)

Solution

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Math Problem Analysis

Mathematical Concepts

Simple Interest
Percentage
Annual Percentage Rate (APR)

Formulas

Total fee = (Amount borrowed / 100) × Fee per $100
Interest Rate = (Total Fee / Principal) × 100
APR = (Interest Rate × Number of 2-week periods in a year)

Theorems

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Suitable Grade Level

Grades 10-12