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Quiz Book

Test your knowledge of financial concepts with this quiz designed by Eng. Ahmed Taha. Questions cover topics like interest rates, investments, loans, and cash flow analysis. Challenge yourself now!

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Quiz Book

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  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. $2000 F=? i = 10% year 1 4 2 $4000 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 The rest of the money is withdrawn after 4 years.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 [-4000+2000(P/F,10%,2)](F/P,10,4) + F = 0  F = $3436.535 • 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. $5,000 year i = 10% A=? 0 1 5 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%. 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 + 1000 + 1000 (P/A,10%,7) = 0  P = 5868.4

  5. $2500 $2000 $1500 $1000 year year 2500 0 0 1 1 2 2 3 3 4 4 i = 10% i = 10% $500 $1000 $1500 Quiz 4 P = 2500 (P/A,10%,4)-500(P/G,10%,4) = 2500 (3.1699)-500(4.3781)  P = $5735.7 • With i=10% find the present value of the series below • Find an equivalent payment A for the series above -solution 1: A = 5735.7 (A/P,10%,4) = $1809 -solution 2: PG = -500(4.3781) A2 = PG (A/P,10%,4) = $ 690.57 Af = 2500-690.57 = $1809.42

  6. $10,000 year i = ?% A=2400 0 1 5 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? 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 = $1996.35

  7. year i = 10% 0 8 11 A=2400 P=? year i = 10% 0 1 n A P=4A 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 = 1626.79 • 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%. P = A(P/A,10%,n) 4A = A(P/A,10%,n)  (P/A,10%,n) = 4 Using extrapolation  n = 5.37 years

  8. $50,000 year i = 10% 8 0 1 A=? 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)–9,372.07 (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

  9. S A year 5 0 1 MARR = 10% P Quiz 8 Consider the following mutually exclusive investment alternatives (MARR=10%): Compare the three alternatives based on PW. Which is better? PWa = -200+22 (P/A,10%,5)+ 200 (P/F,10%,5) = $7.58 PWb = -4,000+600(P/A,10%,5)+ 2,500(P/F,10%,5) = -$173.27 PWb = -5,500+750(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. S A year 5 0 1 MARR = 10% P Quiz 9 Consider the following mutually exclusive investment alternatives (MARR=10%): Which alternatives are feasible based on their ROR • 0 = -200+22 (P/A,i%,5)+200(P/F,i%,5) • Using trial & Error  i=12.57% > MARR • 0 = -4000+620 (P/A,i%,5)+2600(P/F,i%,5) • i=9.74% < MARR (rejected) • 0 = -5400+740 (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. S A year 5 0 1 MARR = 10% P Quiz 9 continued 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. i = 10% year $1,000 5 0 1 i = 10% year $500  0 1 $2,000 Quiz 10 • Which is better: • 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% • PW = -1,000(P/A,10%,5)-2,000(P/F,10%,5) • = -1,000(3.7907)-2,000(0.6209) • = $5032.62 • PW = A/i = -500/0.1 = -$5,000 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. $5,000 A= $500 year 10 0 1 P 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. 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) = $4434.97 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) = $5574.66 (Worse) i= 12%  P = 500(P/A,12%,8)+5000 (P/F,12%,8) = $4503.23 (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) + 2000) = 0.85 Or B/C = (B- O&M)/I = (3000-2000)/(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) = (3000-2000)/ (8000(A/P,10%,8)- 3000(A/F,10%,8) = 0.8

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