Q.4 (1 Mark)
Fairmont Textile has a plant in which employees have been having trouble with carpal
tunnel syndrome (CTS. an inflammation of the nerves that pass through the carpal tunnel,
a tight space
Q.7 (1 Mark)
Suppose that an oil well is expected to produce 100,000 barrels of oil during its first year
in production. However, its subsequent production (yield) is expected to decrease by 10%
over
Equivalence Calculation with Changing
Interest Rates
F=?
Find the balance at the end of year 5.
6%
6%
5%
4%
4%
0
1
2
3
4
5
$400
$300
$500
Solution
n = 1:
$300( F / P , 5% ,1) = $315
n = 2:
$315( F / P
Personal Savings Point of View
!
Situation 1: If you make
four annual deposits of
$100 in your savings
account which earns 10%
annual interest, what equal
annual amount (A) can be
withdrawn over 4
sub
Equal Cash Flow Series
Compound amount factor (Equal Cash Flow
Series)- Find F, Given A, i , N.
F=?
0
1
A
A
N-1
3
2
A
N
A
A
A
F = A+A(1+i) +A(1+i)2+A(1+i)3+.+A(1+i)N-1
F = A[(1+i)N-1)/i] = A(F/A, i, N
Approach: Modify the Interest Rate
! Idea:
Since the cash flows occur every other year,
let's find out the equivalent compound interest rate
that covers the two-year period.
! How: If interest is comp
o
o
Annual interest rate computed as the product of
interest rate per period and the number of periods
per year
Interest rates are normally quoted on an annual
basis
Or Compounding several times withi
Arithmetic - Gradient
Gradient series: A pattern of receipts or disbursements
(expenditure) for a series that has a uniform linear
(arithmetic or constant) or geometric increase in each
time period
(
Summary
PF
F P i , N Compound Amount Factor
FP
P Fi , N Present Worth Factor
A F
F Ai , N Compound Amount Factor (U. Series)
FA
A F i , N Sinking Fund Factor (U. Series)
PA
A P i , N Capital Recovery
Example
Calculate P. Given A=$1000, i=10%, g=8%, N=5
for i g
1 (1 + g ) N (1 + i ) N
P = A
ig
g%
P
A
1 (1.08) 5 (1 + 0.1) 5 0 1 2
P = $1000
0.1 0.08
P = $4,383
If i = 8%, g = 10%. P = $4,804
NA
If i
Arithmetic Gradient Conversion
to Uniform Series
Another Form
A G A 2G
A
0123
N 1
N
The pattern :
A, A G , A 2 G , A 3G ,., A ( N 1)G
N , is the duration of the series
3
Example
A man has purchased a
23/09/2013
Example
Example 6 Multiple Payments Tuition
Tuition
Prepayment
Prepayment Option
Check to See if $107,690 is Enough to
Meet the Future Tuition Needs
0
1
2
3
$107,690
$80,482
$56,599
$29,873
Example
Find Future Worth F. Given: i = 10%, N = 5 yrs.
G = $200
$1200
01
Solution
F
F
F
F
2
3
4
5
= [A(F / A,10%,5)] [$G ( A / G,10%,5)]* (F / A,10%,5)
= 1200(6.105) $200(1.8100)(6.1050)
= $7,326.00
Example 5
Suppose we decided to pay the 6,800 for the time
payment purchase contract in the previous
example (4) what monthly rate of return would
we obtain on our investment?
9
Example
Example 6 Hand
Example
!
On a certain piece of machinery, it is Year
estimated that the maintenance
expense will be as shown. What is
1
the equivalent uniform annual
maintenance cost for the machinery 2
if 6% intere
Present Worth. Note Steps !
Solution
P
( P / A,6%,5)
( P / F ,6%,1)
02
6
10
012
6
10
0
10
P = ($1000 + $100( A / G ,6%,5) )(P / A,6%,5)(P / F ,6%,1)
P = ($1000 + $100(1.88363) )(4.21236 )(0.94340 )
P
Geometric Series
End of Yr.
Amount
1
A(1 + g )0
2
A(1 + g )1
:
:
N
A(1 + g ) N 1
Present Worth
A(1 + g )0
(1 + i)1
A(1 + g )1
(1 + i) 2
A(1 + g ) N 1
(1 + i) N
13
Note:
P / F , i, N =
1
(1 + i ) N
N
1
Continuous Compounding
Continuous Compounding is the ultimate limit for the
number of compounding periods in 1 year.(m infinity)
Starting from:
r
i = 1 +
m
m
1
r
i = lim 1 +
m
m
m
m
m
r r
1 = lim 1 +
Tabular Method
B0 is the starting balance
I1 = B0*i =P *i
PP1 = A - P *i
B1 = B0 - (A-P *i) =P-PP1
At the end of second period
I2 = B1 i = (P-PP1)i
P2 = A (P-PP1)i = (A-Pi) + PP1 i = PP1 (1+i)
B2 = B1
Example
Example 7
Suppose you make equal quarterly deposit of
$1,000 into a fund that pays interest at a rate of
12% compounded monthly. Find the balance at
the end of year three.
Solution
Solution
!
Example
!
!
Suppose that you borrow $5000 with add-on rate
of 12% for 2 years. You will make a 24 equal
monthly payment.
Determine the amount of the monthly installment
Compute the nominal and effecti
Mortgage
!
!
1.
2.
3.
4.
"
A mortgage is generally a long-term amortized loan used primarily to the purpose of
purchasing a piece of property such as home
Types of Mortgages
National Housing Act (NHA)
Example Closed mortgage with prepayment
privileges
Home price = 125,000
Down payment 25,000
Conventional mortgage = 100,000
3 years term 8% per annum
Amortization period of 25 years
Closed mortgage wi