Discrete Mathematics

Chapter 10Money

Percentage

Tipping

• 15% is usually considered a normal tip. How much would you have to tip for a bill:

• $6.40• $0.96

• $154.25• $23.14

• $99.87• $14.98

Simple Interest

• APR: Annual Percentage Rate

• Interest Rate

• Principal

Simple Interest

• Only original money will gain interest

• You have $1000 in a savings account when you open it. The bank gives you a 5% interest rate. After 5 years how much interest will be earned?

• You will have that for 5 years

• After 5 years you will have earned $250

Simple Interest Formula

Saving Bond

• Suppose that you buy an $875 savings bond that pays 4.28% annual simple interest. Determine the future value of the bond after– Four years• $1024.80

– Five years• $1062.25

– Ten years• $1249.50

• Suppose that you buy a $10,000 bond that pays 5% annual simple interest. When you cash in the bond, you have to pay 15% federal taxes on the interest you earned. How much money would you net if you cash in the bond after five years? Round to the nearest penny.

• $12,125

• A loan of $5400 collects simple interest each year for eight years. At the end of that time, a total of $8316 is paid back. Determine the APR for this loan.

• 6.75%

Problems

Page 392 #2-30 even

Compound Interest

• The previous amount is effected by the interest.

$100 at 5% APR

Simple • $105• $110• $125• $150• $200• $250• $300• $350• $400

Compound• $105.00• $110.25• $127.63• $162.89• $265.33• $432.19• $704.00• $1146.74• $1867.92

Annual Compound Formula

Compare Simple and Compound

• Simple

• Annual Compound

Compound Interest

• You want to save for a cruise. You need $2000 but right now you only have $875. You decide to invest it in a savings account that offers 6.75% APR and it is compounded annually. How much will you have in 7.5 years?

• $1382.24

– How much would you have to originally invest?• $1266.06

Compound Monthly

• Now the same bank offers you the same interest rate but compounded MONTHLY. How much will you have saved after 7.5 years?

General Compound Interest

$875 at 6.75%Compounded After 7 years

Annually

Quarterly

Monthly

Daily

Hourly

Minutely

Secondly

Compounded After 7 years

Annually $1382.24

Quarterly $1397.98

Monthly $1401.64

Daily $1403.44

Hourly $1403.50

Minutely $1403.50

Secondly $1403.50

What did you see

• They all approached a number– $1403.50

Continuous Compound Formulaaka PERT

Problems

Page 393 #32-50 even

Fixed Deferred Annuity

• After a child is born the parents decide to put aside $100 a month in a trust fund to help save for college. The interest rate is compounded monthly at 6%. How much will be saved after 18 months?

• T =216

• p = 0.005

• L =100.50

Installment Loans

New Car

• The price of a new car is $23,995. You have a $5,000 down payment and the dealer has two offers that you can choose from. The first is a $2,000 rebate, the second is 0% APR for 60 months. The normal interest rate is 6.48%. Which is the better deal?

• 0% for 60 months– $316.59 to $332.37

Problems

Page 395 #64-80 even