Interest Rates
4C Math
Unit B – Credit Cards, etc
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.
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.
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?
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
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?
Interest
• Three ways interest is calculated:
a) Simple Interest: A = P + Prt
b)Compound Interest: A = P(1+ i)n
c) Continuous Interest: A = Pert
i = interest rate per compounding period, n = compounding
periods in total, P = principal, A = amount, r = yearly interest rate
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?
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.
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?
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?
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?
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?
•
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?