mathematical Analysis
Faculty of commerce English Section
First year
Chapter 9
Matrix Algebra
Definition
A matrix is a rectangular array of real numbers, which is enclosed in large brackets. Matrices
mathematics of finance
Faculty of commerce English Section
Second year
EX 4 -a
Ordinary annuities
3: Every 3 months a person puts $100 in a savings account that pays 5% compounded
quarterly. If the fi
Faculty of commerce English Section
Second year
mathematics of finance
Chapter 5-a
Other annuities Certain
Finding the term of an annuity
Sn (due) = Rs n+1-1 = Rs n(1+i) = R
An (due) = Ra n-1+1 = Ra n
Faculty of commerce English Section
Second year
mathematics of finance
Chapter 4-e
Ordinary annuity
Finding the term of an annuity
n = log (Sni/R + 1)
log (1 + i)
n = - log (1 - Ani/R)
log (1 + i)
Exa
Faculty of commerce English Section
Second year
mathematics of finance
Chapter 5-c
Other annuities certain
Deferred annuity
A deferred annuity is one in which the first payment is made not at the begi
mathematics of finance
Faculty of commerce English Section
Second year
Chapter 4
Ordinary annuities
ANNUITY OF SIMPLE INTEREST
Ordinary Annuity
R
R
R
R
Annuity due
R
R
R
R
R
R
R
The amount
Sn= Rn+ n /
mathematics of finance
Exercise 4 - D
Ordinary annuity
Faculty of commerce English Section
Second year
3: A family buys a washer that sells for $450 cash. They pay $50 down and the balance
in 12 equal
Faculty of commerce English Section
Second year
mathematics of finance
Chapter 4-f
Ordinary annuity
Finding the interest rate
Example 1: find the rate per period and the nominal rate converted quarter
mathematics of finance
Faculty of commerce English Section
Second year
Chapter 4
Ordinary annuities
When most people buy a home, they borrow money and agree to repay it in monthly payments over a peri
Faculty of commerce English Section
Second year
mathematics of finance
Chapter 4-d
Ordinary annuity
Periodic payment of an annuity
R=Sn/ sn= Sn
i
(1+i) n - 1
R=An/ an= An
i
1-(1+i) -n
Example 1: If mo
Faculty of commerce English Section
Second year
mathematics of finance
EX 4 -b
Ordinary annuities
5: If money is worth 9% converted semiannually, what is the present value of $10,000
due at the end of
mathematics of finance
Faculty of commerce English Section
Second year
Chapter 4-b
An = Ran= R
Ordinary annuities
1- (1+i) -n
i
An = Present value of an ordinary annuity of n payments
R= Periodic paym
mathematics of finance
Exercise 3 C
Compound interest
Faculty of commerce English Section
Second year
1: On June 30, 1987, Charles Moser borrowed $3,000 at 8% converted semiannually. How
much must he
Faculty of commerce English Section
Second year
mathematics of finance
Chapter 2
Bank Discount
The charge for many loans is based on the final amount rather than on the present value. This charge is
c
mathematics of finance
Exercise 3 g
Compound interest
Faculty of commerce English Section
Second year
1: How long will it take an investment to increase at least 50% in dollar value if the
interest ra
Faculty of commerce English Section
Second year
mathematics of finance
Chapter 3-C
Compound Interest
Interest for part of a period
When there is a part of a period, the usual practice is to allow simp
Faculty of commerce English Section
Second year
mathematics of finance
Chapter 3-a
Compound Interest
S = P (1 + i) n
S = the amount at compound interest
P= the principal
i= the rate per conversion per
Faculty of commerce English Section
Second year
mathematics of finance
Chapter 3-b
Compound Interest
The effective rate is the rate converted annually that will produce the same amount of interest per
mathematics of finance
Exercise 2 a
Simple interest
Faculty of commerce English Section
Second year
1: Determine the bank discount and the proceeds if $1500 is discounted for 3 months at
a discount ra
Faculty of commerce English Section
Second year
mathematics of finance
Chapter 3-h
Compound Interest
Equation of value
Example 1: A person owes $20,000 due in 1 year and $30,000 due in 2 years. The le
Faculty of commerce English Section
Second year
mathematics of finance
Chapter 3-g
Compound Interest
Finding the Time
Example 1: How long will it take $200 to amount to $350 at 7% compounded
semiannua
mathematics of finance
Faculty of commerce English Section
Second year
Chapter 3-i
Compound Interest
Example 1: A new car cost $12,000 and depreciates 25% a year. Find the book value at
the end of eac
mathematics of finance
Exercise 3 a
Compound interest
Faculty of commerce English Section
Second year
1: A finance company makes consumer loans at a nominal annual rate of 36%
compounded monthly. Find
mathematics of finance
Exercise 3 - h
Compound interest
Faculty of commerce English Section
Second year
1: A person owes $30,000 due in 2 years and $50,000 due in 4 years. If money is worth
7% convert
Faculty of commerce English Section
Second year
mathematics of finance
Chapter 3-D
Compound Interest
Present value at compound interest
To find the present value of a future amount:-
P = S / (1 + i) n
mathematics of finance
Exercise 3 b
Compound interest
Faculty of commerce English Section
Second year
1: What is the effective rate of interest equivalent to 10% converted?
(a) Semiannually?
(b) Quart
mathematics of finance
Faculty of commerce English Section
Second year
Chapter 3-f
Compound Interest
Finding the rate
Example 1: If $500 amounts to $700 in 5 years with interest compounded quarterly,
mathematics of finance
Faculty of commerce English Section
Second year
Review Problems
Derive the formula Sn (for) = R[(1+i)n+p (1+i)p]/ i
(Sn (for
.
.
1
n-2
n-1
n
1
2
3
Payment interval of n periods
mathematics of finance
Chapter 1
Simple interest
Faculty of commerce English Section
Second year
Example 7: A woman borrows $2000 from a credit union. Each month she is to pay $100
on the principal. S