MENTAL STRENGHT
Mental strength is one of the things that we humans lack. As an athlete, I lack mental strength
sometimes and that is prevalent. Mental strength is something that can be learned. When someone
thinks negative of themselves all the time, the
Problems
inflation-free interest rate (i' ) will be 6% and
the general inflation rate I 5 %. If the plant
has a remaining useful life of five years. what is
the present equivalent value of its fuel costs,
using actual-dollar analysis?
4.14
4.17
A father w
Problems
2. Calculate the present worth of constant dollars by discounting at i'.
Adjusted-discount methodone step (use the market interest rate):
A
where
Alternatively, just use the market interest rate to find the net present
\ r/c: In these pi oblems.
4
VECTORS and SCALARS
SOLVED PROBLEMS
1. State which of the following are scalars and which are vectors.
(a) weight
(c) specific heat (e) density (g) volume
(i) speed
(f) energy
(b) calorie (d) momentum
(h) distance (j) magnetic field intensity
Ans. (a) v
VECTORS and SCALARS
g
18. Let P. , P2 P3 be points fixed relative to an origin 0 and let r1, r2, r3 be position vectors from
0 to each point. Show that if the vector equation alrl + a2r2 + a3r3 = 0 holds with respect to
origin 0 then it will hold with res
A VECTOR is a quantity having both magiiitud and direction such as di splacement,_ velocity, force
and acceleration.
Graphically a vector is represented by an arrow OP (Fig.l) defining the direction, the magnitude of the vector being indicated by
the leng
The DOT and CROSS PRODUCT
A1B1 + A2B2 + A3B3
=
since
7.
ii =jj=kk=1
and all other dot products are zero.
If A = A1i + A2j + A3k, show that A = A =
Al + A2 + A2
Then A = VIA A.
(A)(A) cos 0 = A2.
Also,
19
A A = (A1i +A2j +A3k) (A1i +A2j +A3k)
_ (A1)(A1) +
VECTORS and SCALARS
14
37. If ABCDEF are the vertices of a regular hexagon, find the resultant of the forces represented by the vec-
tors AB, AC, AD, AE and AF.
Ans. 3 AD
38. If A and B are given vectors show that (a) I A+ B I
39. Show that
I A I+ I B I,
107
Problems
3.36
What is the required quarterly payment to
repay a loan of $20,000 in 20 years if the interest rate is 8% compounded continuously?
3.37 A series of equal quarterly payments of
$1,500
extends over a period of 20 years. What is the
present
Problems
2 A restaurant is considering purchasing the lot adjacent
to
its business to provide adequate parking space for its
customers. The i restaurant needs to borrow $44,000 to
secure the lot. A deal has been made between a local
bank and the restauran
1O4
CHAPTER 3
Understanding Money Management
(b)
What is the future worth of the
$8,50
series of payments'?
0 following
in
15
(a) $5,000 at the end of each six-month period
years
for 10 years at 4% compounded
at
comp semiannually.
(b) $9.000 at the end of
Problems
3.1
8
pays 8% interest compounded quarterly. How
much money will be in each account six years
after the transfer?
A series of equal quarterly deposits of $1.000
extends over a period of three years. It is desired to compute the future worth of th
Problems
103
where r the APR. M the number of compounding periods, and
i = the effective interest rate.
In any equivalence problem. the interest rate to use is the effective interest
rate per payment period, which is expressed as
Where C the number of int
Problems
original bank note was for $4,800, with an interest rate of 12% compounded monthly. After l6
monthly payments, David found himself in a financial bind and went to a loan company for assistance in lowering his monthly payments.
Fortunately, the lo
Problems
(a) Compute the
Option 1.
monthly payment
for
(b) What is the effective annual interest
rate you are paying for Option 2?
Compute the outstanding balance for
each option at the end of five years.
(d) Compute the total interest payment for
each op
Problems
103
where r the APR. M the number of compounding periods, and
i = the effective interest rate.
In any equivalence problem. the interest rate to use is the effective interest
rate per payment period, which is expressed as
Where C the number of int
Problems
(a) Compute the
3.62
monthly payment for
Option 1.
(b) What is the effective annual interest
rate you are paying for Option 2?
Compute the outstanding balance for
each option at the end of five years.
(d) Compute the total interest payment for
ea
Problems
103
where r the APR. M the number of compounding periods, and
i = the effective interest rate.
In any equivalence problem. the interest rate to use is the effective interest
rate per payment period, which is expressed as
Where C the number of int
Problems
3.36 What is the required quarterly payment to
repay a loan of $20,000 in 20 years if the
in- terest rate is
8%
compounded
continuously?
3.37
A series of equal quarterly payments of $1,500
extends over a period of 20 years. What is the
present wo
CHAPTER 2
Time Value of Money
be in the account immediately after the fifth
(c) C = $394.65.
deposit.
(d) C = $458.90.
2.36 Five annual deposits in the amounts of
End of
$1,200,
$1,000, $800, $600, and $400 are made into a
fund that pays interest at a rat
CHAPTER 2
Time Value of Money
be in the account immediately after the fifth
(c) C = $394.65.
deposit.
(d) C = $458.90.
2.36 Five annual deposits in the amounts of $1,200,
$1,000, $800, $600, and $400 are made into a
fund that pays interest at a rate of 9%
70
CHAPTER 2
Time Value of Money
five years (with the first payment at the end of
year six). If the interest rate is 8% compounded annually, what is Bos contract worth at the
time of contract signing?
2.22 You are prepairing to buy a vacation home five
ye
Problems
(a) $5,000 at the end of each year for six years
at 6% compounded annually.
(b) $9,000 at the end of each year for nine
years at 7.25 % compounded annually.
(c) $12,000 at the end of each year for 25
years at 8% compounded annually.
(d) $6,000 at
CHAPTER 2
Time Value of Money
You have $10,000 available for investment in
stock. You are looking for a growth stock that
can grow your investment to $35,000 over five
years. What kind of growth rate are you looking for'?
$100
Short Case Studies with Exce
CHAPTER 2
Time Value of Money
3. Linear gradient series: A series of flows increasing or decreasing by a fixed
amount at regular intervals. Excel is one of the most convenient tools to
solve this type of cash flow series.
4. Geometric gradient series: A s