Discrete Mathematics Chapter 10 Money. Percentage.
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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
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