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A summary of the key concepts covered in exam iii of a mathematics course. Topics include simple and compound interest, time value of money calculations, linear equations, and matrix operations. Examples are included to illustrate the application of these concepts.
What you will learn
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else's money (bank charges you when you borrow; bank charges themselves when you save)
or initial amount, r=interest rate as a decimal, t=time)
terest over time (formula: A = P
r m
)mt
(m=number of compoundings per year)
P ert
earned per year when compounded
to or removed from the account throughout);
you make given periodic deposits to an account (in- terest earned at the same time as each deposit). (EXAMPLES: IRA, 401(k))
make periodic deposits into an account to achieve a given nal amount over a given time period.
Solver, PV=0 (usually); one of PMT or FV is given, and we solve for the other)
drawals on an account for a given amount of time, at least how much money must initially be in the account to accomplish this? (Given PMT with FV=0, nd PV)
order to kill a given debt over a given amount of time (Given PV with FV=0, nd PMT)
your house (Cost of house − Remaining Balance)
home quiz ): When you buy a house, you pay a lot of extra legal fees up front called closing costs. Points are extra fees you pay up front to lower your interest rate slightly. (In both cases ex- tra means they do NOT change the price of your house!)
ten as
A 1 x 1 + A 2 x 2 + · · · + Anxn = b
can perform on a system of equations (rows of the matrix) to create an equivalent system of equa- tions:
ber
add/subtract to another row.
rest of the column):
(if zero, switch rst)
another row and subtract from that row. (do this for each of the other rows in the matrix)
[A|B] in the calculator, then rref the matrix
system of equations has no solution
tem of equations has an innite number of solutions
not have the Goal stated in 4.3 above)
variables
ith row and jth column of A.
all i and j
the corresponding elements (matrices must be the same size)
element by the scalar
ing the rows and columns
and a column matrix
b 1 b 2 · · · bn
is given by a 1 b 1 +
a 2 b 2 + · · · + anbn (must be the same length)
ith row of A and the jth column of B (number of columns in A must equal the number of rows in B)
such that AB = BA = I (where I is the n × n identity matrix). We write B = A−^1.
a singular matrix.
inverse, then X = A−^1 B
the end of 2 years, you pay back $531. How much did you originally borrow?
mortgage at 3.75%. Later, we will learn that your monthly payments are $625.21. What is the new balance on your loan after one month?
$10,000 in an account which earned about 3.5% per year compounded quarterly. How much money was in the account when you turned 18? How much interest did the account earn?
attend A&M was $1,948. Today it is about $10,400 (Sources: www.collegecalc.org and tu- ition.tamu.edu). To the nearest 0.1%, what is the annual increase in tuition?
$140/quarter into an account which earned about 3.5% per year compounded quarterly.
you turned 18?
forego your 3 lattes/week and contribute the $50/month you save into a high-risk fund which earns 7.5% per year compounded monthly.
when you retire in 45 years?
on the account?
ing the 8th month of the 42nd year?
$8.25M, to be paid in 30 equal annual payments. Their interest factor is 1.4108%. How much money needs to be in their account initially in order to pay a winner?
car dealership oers you a no down payment op- tion, nancing the entire amount at 4.9% per year compounded monthly for 6 years.
table for the car you bought in the previous example: Period Payment Interest Principal Balance 0 1 2 3
the principal?
moMonopolCorp.com at 22 with a monthly salary of $4500.
what will your monthly salary be when you retire in 48 years?
ter retirement for 15 years, how much money should you have in your 401(k) when you re- tire if it is in a conservative fund which earns 3% per year compounded monthly?