In many situations, a stated interest rate is often not the effective interest rate. An annual percentage rate (APR) is a stated interest rate. For example, a car loan with 12% APR financing does not have an effective annual interest rate of 12%. This is because the APR is only used for calculating the effective monthly interest rate, which is 1%. The future value of one dollar one year from now, compounded monthly at 1%, is (1+.01)12 = $1.1268. Therefore the effective annual interest rate is 12.68%, but not 12%. The difference is not too large though. But the following are two real-world examples of misleading advertisements on the interest rate for loans.
a. A discount interest loan is a loan that deducts the interest from the principal immediately after it is issued. For example, a 10% one month discount interest loan of $1000 specifies that a borrower takes out $900 but has to repay $1000 in one month. In other words, $100, which is 10% of the principal, is discounted on the outset. Is the monthly interest rate 10%? What is the effective monthly interest rate of this loan? What is the true APR for this loan? What is the effective annual interest rate of this loan?
b. Imagine that you see an advertisement that reads something like this: “$1,000 Instant Credit! 16% Simple Interest! Three Years to Pay! Low, Low Monthly Payments!” You’re not exactly sure what all this means, so you ask the manager for clarification. She explains that if you borrow $1,000 for three years at 16 percent interest, in three years you will owe: $1,000 × 1.163 = $1,000 × 1.56090 = $1,560.90 She recognizes that coming up with $1,560.90 all at once might be a strain, so she lets you make “low, low monthly payments” of $1,560.90/36 = $43.36 per month, even though this is extra bookkeeping work for her. Is this a 16 percent loan? Why or why not? What is the effective monthly interest rate on this loan? What is the APR on this loan? Why do you think this is called add-on interest?
Please show all work for both parts,