Simple interest
$2400 is invested for 6 months at a simple interest rate of 5%. How much interest is earned?
$60
2400(.5*.05)=60
Logan had to take out a loan of $10,000 to gamble in Vegas and double it (hopefully). He plans to pay it off in 2 years with 30% interest compounded monthly. How cooked is he (How much interest is he paying)?
$8,087.26
10000(1+.3/12)^2(12)
Find the corner points given these parameters.
x+y≤10
2x+y≤14
x≥0 y≥0
(0,0),(7,0),(0,10), and (4,6)
Bonus: Find the max and min
Future value given payments of $300 with an interest rate of 8% compounded quarterly for 5 years.
$7,289.21
calculator or equation method
$6700 is invested for 18 months at a simple interest rate of 12%. What is the final amount after the 18 months?
$7906
6700+6700(.12*1.5)
Mr. Clean needs to take out a Loan of 2000 dollars to buy a white Ferrari. He plans to pay off this loan in a year with an interest rate of 2% compounded semiannually. How much interest is he paying in total?
2000(1+.02/2)^1*2= 2040.2
2040.20-2000=40.20
$40.20
What do the inequalities x<3 and y>3 look like?
dotted vertical line at x=3 shaded to the left
dotted horizontal line at y=3 shaded up
Present value given payments of $500 and interest of 6% compounded weekly for 4 years. (52-week year)
$92,414.10
Equation or calculator method
4 years
60=300(.05t)
or
360=300+300(.05t)
60/300=.05t
.2/.05=t
t=4
Find the effective rate corresponding to 5% compounded monthly. Round to the nearest hundredth of a percent.
%5.12
(1(1+.05/12)^12*1)-1=.051161
Maximize
P=4x+3y
x+y≤10
x+2y≤16
x≥0
y≥0
(0,0) =0
(10,0)= 40
(0,8)= 24
(4,6)= 34
Maximum of 40 at (10,0) use the graphing method of corners.
To help finance the purchase of a new mansion, you secured a loan from the bank at a rate of 12% a year compounded monthly. You are required to make payments of $4000 for 40 months. What is the price of your new mansion?
131,338.74
calculator or equation method
A bank deposit paying simple interest grew from an initial sum of $500 to $570 in 24 months. Find the rate.
.07 or 7%
570=500+500(2I)
70=500(2I)
70/500=2I
70/1000=I
70/1000=.07
Remy the rat wants to open a new restaurant, and because he is a rat, the city of Paris (grr the French) is making him pay a fine of $10,000 over the course of 3 years, with a rate of 20% compounded semiannually. How much is Remy paying in total for this discriminatory fine?
10,000(1+.2/2)^3*2
$17,715.61
Minimize
C=3x+5y
x+2y≥10
3x+y≥12
x,y≥0
x+2y=10
3x+y=12
(0,12)=60
(2.8,3.6)=26.4
(10,0)=30
(2.8,3.6)=26.4 is the min use method of corners and graph
After losing all his coins in a near-fatal car crash while speeding, Sonic decides to invest a large sum of $50,000 into the bank at a rate of 7% per year compounded quarterly. In addition to this, every month Sonic will make a payment of $2. If Sonic keeps this up for 2 years, how much interest will he have earned?
57461.10= total
57461.10-50000+2(8)=7445.10
Sonic earned $7445.10 (which he lost in a car crash 2 days later)
How much interest is going to be earned on $6000 deposited into a bank 6 years ago with a simple interest rate of 10%?
6000(.1*6)
$3600
Yoshi invests 30 dollars in the bank for his kid's college at the Mushroom Kingdom University. He plans to take this amount out after letting it sit in the bank for 10 years at a rate of 10% compounded daily. How much money will Yoshi receive when he decides to take out his money from the bank?
$81.54
30(1+.1/365)^10(365)
The Bread Company produces two types of bread, Yummy Honey and Gross Sourdough. The Honey bread requires 5 hours to make and 0.5 hours to bag, and the Sourdough bread requires 3 hours to assemble and 1 hour to bag. The maximum number of bread-making hours available is 24 per day, and the maximum number of bagging hours available is 13 per day. Let x represent the number of Honey bread, and y represent the number of Sourdough bread. Write the system of inequalities that describes the constraints on the number of each type of bread produced.
5x+3y less than or equal to 24
.5x+y less than or equal to 13
x and y are greater than 0
Bowser intends to sue Mario for defamation. In order to do this, he is investing in the best lawyer (Saul Goodman). However, Saul is even bigger and greedier than Bowser, so he is charging $1,000,000 more than his normal price of $50,000, which he claims is for inflation. Bowser is only wealthy in terms of shelled companions (turts), so he intends to take out a loan, which he will pay over the course of 4 years with an interest rate of 4% compounded monthly. If Bowser plans to make payments every month, how much are his payments, assuming he can make a down payment of 3 dollars to Saul?
$23,707.94
calculator or equation method