1. Quiz Book
Summer 2003
Prepared by:
Eng. Ahmed Taha

2. Quiz 1
Considering the class policies, indicate whether each of the following statements is True (T) or False (F) by circling T or F next to each statement

3. Quiz 2 Depict the following transactions on a cash flow diagram:
Depositing $4,000 today and withdrawing $2,000 after two years. The rest of the money is withdrawn after 4 years. If the interest rate is 10%, how much money will be available for the last withdrawal
[ (P/F,10%,2)](F/P,10,4) + F = 0
 F = $ 1 4 2
i = 10%
F=?
year
$4000
$2000
How long would it take for $200 to double if the interest rate is 12%?
400 = 200(F/P,12%,n)
 (F/P,12%,n) = 2
Using interpolation
n = 6.11 years (almost 6 years & 1 month)

4. Quiz 3
Determine the annual installments of a loan of $5,000 to be paid in 5 equal end-of-year payments if the interest rate is 10%. 1 5
A=?
i = 10%
$5,000
year
A = P (A/P,10%,5)
A = 5000 (0.2638)
 A = $1319
Find P in the graph to the right assuming that A = $1,000, and i = 10%
-P (P/A,10%,7) = 0
 P =

5. Quiz 4 With i=10% find the present value of the series below1 4 2 3
i = 10%
year
$2500
$2000
$1500
$1000
P = 2500 (P/A,10%,4)-500(P/G,10%,4)
= 2500 (3.1699)-500(4.3781)
 P = $5735.7 1 4 2 3
i = 10%
year
$500
$1500
$1000
2500
Find an equivalent payment A for the series above
-solution 1:
A = (A/P,10%,4) = $1809
-solution 2:
PG = -500(4.3781)
A2 = PG (A/P,10%,4) = $
Af = = $

6. Quiz 5
What interest rate is being charged if a loan of $10,000 received today is to be repaid in 5 equal end-of-year payments of $2400 each? 1 5
A=2400
i = ?%
$10,000
year
P = A (P/A,i%,5)
10,000 = 2400 (P/A,i%,5)
 (P/A,i%,5) = 4.167
using interpolation
 i= 6.4%
Which is better, to buy a computer by paying $2,000 immediately, or by paying 5 equal end-of-year payments of $2400 each, if you can invest your money at 8%? Why?
Five equal payments would be slightly better.
P = A(P/A,8%,5)
P = 500 (P/A,8%,5)
 P = $

7. Quiz 6
What lump sum would have to be deposited today into an account bearing interest of 10% per year to provide withdrawals of $1000 8,9,10,11 years from today?
P = 1000(P/A,10%,4)(P/F,10%,7)
 P = 11 8
A=2400
i = 10%
P=?
year
How many years will it take for a uniform annual deposit of size A to have the same value as a single deposit now that is 4 times the size of one annual deposit? Assume that i = 10%. n 1 A
i = 10%
P=4A
year
P = A(P/A,10%,n)
4A = A(P/A,10%,n)  (P/A,10%,n) = 4
Using extrapolation  n = 5.37 years

8. Quiz 7
A loan of $50,000 is to be repaid in 8 equal end-of-year payments at 10%
Find the value of the installments
After 3 years, how much of the loan would be paid?
How much would it cost to buy down the interest to 9%?
A= 50,000(A/P,10%,8) = $9,372.07
X =50,000(F/P,10%,3)–9, (F/A,10%,3)
 X = $35,528.44
Paid amount = 50,000- X = $14,417.56
A1 = 50,000(A/P,10%,8) = $9,372.07
A2 = 50,000(A/P,9%,8) = $9,033.42
 Cost = (A1- A2) (A/P,9%,8)= $1,874.41 8
A=?
i = 10%
year
$50,000 1

9. Quiz 8 Consider the following mutually exclusive5 A
MARR = 10%
year S 1 P
Consider the following mutually exclusive
investment alternatives (MARR=10%):
Compare the three alternatives based on
PW. Which is better?
PWa = (P/A,10%,5)+
200 (P/F,10%,5) = $7.58
PWb = -4, (P/A,10%,5)+ 2,500(P/F,10%,5)
= -$173.27
PWb = -5, (P/A,10%,5)+ 4,500(P/F,10%,5)
= $137.15
Without performing any calculations, which of B&C have a higher ROR? C

10. Quiz 9 Consider the following mutually exclusive5 A
MARR = 10%
year S 1 P
Consider the following mutually exclusive
investment alternatives (MARR=10%):
Which alternatives are feasible
based on their ROR
0 = (P/A,i%,5)+200(P/F,i%,5)
Using trial & Error  i=12.57% > MARR
0 = (P/A,i%,5)+2600(P/F,i%,5)
i=9.74% < MARR (rejected)
0 = (P/A,i%,5)+4300(P/F,i%,5)
 i=10.13% > MARR
See next slide for the best alternative based on the ROR?

11. Quiz 9 continued 5 A
MARR = 10%
year S 1 P
To determine which of A or C is better we must calculate the ROR based on the difference .
i = 10.03%
Based on this, we may say that C is better than A, or that the difference is too small and for all practical purposes we may consider them equivalent. In other words, doing A and investing the rest at 10% is almost the same as doing C.

12. Quiz 10 Which is better: a 5 PW = -1,000(P/A,10%,5)-2,000(P/F,10%,5)
4 end-of-year receipts of $1,000each, and a on time receipt of $3,000 at the end of the fifth year.
$500 annually forever assuming that the prevalent interest rate is 10% 5
$1,000
i = 10%
year
$2,000 1
PW = -1,000(P/A,10%,5)-2,000(P/F,10%,5)
= -1,000(3.7907)-2,000(0.6209)
= $
PW = A/i = -500/0.1 = -$5,000 
$500
i = 10%
year 1 a
II. Find the discounted payback period of the cash flow diagram to the right assuming P= $5,000, A=$1,400, and MARR = 10%. Draw the investment balance diagram. 5

13. Quiz 11
A bond with a face value of $5,000 pays interest of 10% per year will be redeemed at a par value at the end of its 10-year life. How much should be paid for this bond now in order to yield:
8% per year.
12% per year. 10
A= $500
year
$5,000 1 P
A = 5000(0.1)=500
i= 8%  P = 500(P/A,8%,10)+5000 (P/F,8%,10) = $5671
i= 12%  P = 500(P/A,12%,10)+5000 (P/F,12%,10) = $
In both cases above, if the bond had a life of 8 years, would it be better(higher PW) or worse?
i= 8%  P = 500(P/A,8%,8)+5000 (P/F,8%,8) = $ (Worse)
i= 12%  P = 500(P/A,12%,8)+5000 (P/F,12%,8) = $ (Better)

14. Quiz 12
What is the B/C ratio of an investment that requires an initial payment of $8,000 in return for equal end-of-year returns of $3,000 for 8 years, if the O&M expenses are $2,000? Assume i=10%.
I = $8,000 B = $3,000 O&M = $2,000
B/C = B/(I+O&M) = 3000/(8000(A/P,10%,8) ) = 0.85 Or
B/C = (B- O&M)/I = ( )/(8000(A/P,10%,8)) = 0.66
How would your answer changes if a salvage value of $3,000 is expected
B/C = B/(I-S+O&M) = 3000/ (8000(A/P,10%,8)- 3000(A/F,10%,8) +2000) = 0.92 Or
B/C = (B-O&M)/(I-S) = ( )/ (8000(A/P,10%,8)- 3000(A/F,10%,8) = 0.8