Section F.4, 4.3, 4.4
MATH 166:503
March 31, 2015
Topics from last notes: Simple interest, present value of simple interst loan, discount loans,
effective rate of a discounted loan, compound interest, effective yield, present value of compounded
loan, annuities, future value of an annuity, sinking funds, interest per period in a sinking fund
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FINANCE
1.4
Present Value of Annuities and Amortization
ex. You are renting a new apartment for one year, starting next month, at a rate of $385 per
month. You found a bank account that offers a two year promotional annual interest rate of 8%,
compounded monthly. What amount of money should you invest today in order to be able to make
all rent payments (and not have any money remaining)?
In general,
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ex. You paid a $2500 down payment on a used car. In order to pay the rest of the balance, you
got a loan from the bank at an annual interest rate of 15%, compounded quarterly. To pay off this
loan, you agreed to make payments of $450 every quarter for 10 years. What is the cash price of
the car? What is the price you’re actually paying for the car?
Def: amortization is
ex. If you have $30,000 in student loans in an account with a nominal interest rate of 18%,
compounded monthly. What does your monthly payment need to be in order to pay off the loan
in 5 years?
What is the amount paid towards the principal in the first month? What is the remaining
principal?
In the second month?
In the first year?
2
In general,
4
SYSTEMS OF LINEAR EQUATIONS AND MODELS
4.3
Gauss Elimination for Systems of Linear Equations &
4.4
Systems of Linear Equations with Non-Unique Solutions
ex. Suppose you wanted to buy your 6 closest friends a gift. You want to give your friends either
a bouquet of flowers, which costs $5, or a bar of chocolate, which costs $3.75. You have $25 to
spend. How many of each gift can you get?
The rules:
1.
2.
3.
What is the picture?
3
ex. A company produces three products: a dress shirt, a casual shirt, and a sport shirt. Each shirt
requires the use of a sewing machine, cutting machine, and packing machine. An order of dress
shirts requires 3 hours on the cutting machine and 2 hours on the sewing machine. An order of
casual shirts requires 5 hours on the cutting machin and 1 hour on the sewing machine. An order of
sport shirts requires 7 hours on the cutting machine and 3 hours on the sewing machine. All orders
of shirts requires 2 hours on the packing machine. If the cutting machine is available for 480 hours,
the sewing machine for 170 hours, and the packinging machine for 200 hours, how many orders of
each type of shirt should be produced to use all of the available time on the three machines?
What is the picture?
4
ex. A bakery is only planning on making cookies, cakes, and cupcakes tomorrow. The bakery has
80 cups of butter, 91 cups of flour, and 78 cups of sugar. The following tables displays the required
amount of ingredients needed for these products.
butter (cups)
batch of cookies
batch of cakes
batch of cupcakes
1
4
1
2
1
sugar (cups)
1
1
2
flour (cups)
2
4
8
How many batches of each product can be made in order to use all of the given ingredients?
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ex. Compute (x, y, z) for the following system of linear equations
3x + 9y + 15z = 21
x + 10z = 18
x + 3y + 5z = 7.
ex. A bakery is only planning on making cookies, cakes, and cupcakes tomorrow. Now assume the
bakery has 36 cups of butter, 91 cups of flour, and 78 cups of sugar. The following tables displays
the required amount of ingredients needed for these products.
butter (cups)
batch of cookies
batch of cakes
batch of cupcakes
1
4
1
2
1
sugar (cups)
1
1
2
flour (cups)
2
4
8
How many batches of each product can be made in order to use all of the given ingredients?
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