1. Interest Rates 4C Math Unit B – Credit Cards, etc

2. Cuts and Raises To compute cuts or raises we multiply our old price or salary by the percentage. Then we add or subtract (add in the case of a raise, subtract in the case of a cut) this number to our old price or salary. Example B1: If you make $35,000 per year and receive a 5% raise what is your new salary? 5% of your income is.05 x 35,000 = $1750. Getting a 5% raise means your new salary is.05 x 35,000 plus your old salary. So your new salary is $35,000 + $1750 = $36,750. Notice that, just like sales tax, we could have simply multiplied our old salary by 1.05 to get our salary after the raise.

3. Cuts and Raises However, to compute a pay cut we need to multiply by 1 minus the percent. This is illustrated in the next example. Example B2: If you make $72,000 per year and receive a 9% pay cut. What is your new salary? New salary = $72,000 -.09 x $72,000 = $72,000-$6480=$65,520. Or using 1 – 0.09: New salary = (1-0.09) x $72,000 =.91 x $72,000 = $65,520.

4. Cuts and Raises Exercise: Suppose your boss tells you that “for bookkeeping purposes” you are going to receive a 20% pay cut followed by a 20% pay raise. Do you end up with the same salary after the raise and cut? What if he gave you a 20% pay raise followed by a 20% pay cut? Are you happy either way?

5. Cuts and Raises Example C: A clothing store is having a 30% off sale. The sale price of a sweater is $60. What was the pre-sale price? Caution!! We don’t take 30% of $60 and add that to $60. This is because the discount is 30% of the pre-sale price. What do we do? Well…if P is the pre-sale price then we have: $60 = P – 30% of P = P - 0.3 x P. Then $60 = (1-0.3) x P and so $60 = 0.7 x P. To find P we just divide $60 by 0.7. Thus the pre-sale price was P = 60/(1 – 0.3) = $85.71

6. Cuts and Raises Example D: Suppose you paid $1100 to insure your car this year and the cost of insurance will go up 10% next year. What will you owe for car insurance next year?

7. Interest Three ways interest is calculated: a) Simple Interest: A = P + Prt b) Compound Interest: A = P(1+ i) n c) Continuous Interest: A = Pe rt i = interest rate per compounding period, n = compounding periods in total, P = principal, A = amount, r = yearly interest rate

8. Interest Example: Suppose we invest $1000 in an account and let it sit. How much is in our account at the end of 2 years if the account has an annual rate of 4% and uses: (a) simple interest? (b) interest compounded monthly? (c) interest compounded daily?

9. Interest The difference between the 3 types of interest: simple interest is computed once per year, compounded interest is computed every period, while continuously compounded interest is computed continuously (or every instant). Bank Accounts: The typical savings account computes interest by compounding continuously. Credit Cards: The typical credit card computes interest by compounding daily.

10. Credit Cards Example: Suppose your Discover Card has a previous balance of $6000 and APR of 12.74%. What is the daily periodic rate? What will the finance charges be this month? What is your new account balance?

11. Credit Cards Example: Suppose your Discover Card has a previous balance of $6000 and APR of 12.74%. Discover Card computes your minimum payment by taking the larger of a) the closest whole number to 2% of your balance and b) $15. How much will this months minimum payment be?

12. Credit Cards Example: Suppose your Discover Card has a previous balance of $6000 and APR of 12.74%. If you pay the minimum payment how much of your payment is going towards paying down your original $6000 balance?

13. Credit Cards Example: Suppose your Discover Card has a previous balance of $6000 and APR of 12.74%. Discover Card agrees to waive any fees for missing payments. So you decide to not pay anything on your card for a whole year. What is the balance on your card after the year is up?

14. Credit Cards Exercise: Suppose MasterCard gives you a card with 17% APR and no fees for missing payments. You purchase a new snowboard and gear for $500 on your MasterCard. What will the first month’s finance charges be? If you don’t make payments or new purchases for a year what is your new account balance?