ACFI201 Practice Questions
XXXXXX Suppose you invest $1,000 in an account paying 8% p.a. interest with annual compounding. b) Which do you prefer: a bank account that pays 5% p.a. (EAR) for three years or i. 2.5 % every six months for 3 years ii. 7.5 % every 18 months for 3 years iii. 0.5 % per month for 3 years XXXXXXX
XXXXXXX EAR= (1+ (APR/m))∧m -1 i) EAR = (1+(2.5/2))² -1 EAR = 4.0625 ii) EAR = (1+(7.5/0.6666))∧0.666 -1 EAR = 4.314 iii) EAR = (1+(0.5/12))¹²-1 EAR= 0.632 XXXXXXX
Marty wants to rank the following alternatives assuming he can earn 5% p.a. a) $180 received in one year b) $220 received in five years c) $300 received in ten years
present value of a future cash flow a) PV = 180/(1.05)¹ PV = 171.429 b) PV = 220/(1.05)⁵ PV= 172.376 c) PV = 300/(1.05)¹⁰ PV= 184.174
Suppose you invest $1,000 in an account paying 8% p.a. interest with annual compounding. a) What is the balance in the account after 25 years? How much of this balance corresponds to interest on interest?
future value of present cash flow a) FV = 1000 x (1.08)²⁵ FV = 6848.475 simple interest = 1000x0.08x25 =2000 principle investment = 1000 interest on interest = 6848.475-2000-1000 =3848.475
INTEREST RATE Your bank is offering you an account that will pay 20% interest in total for a two-year deposit. Determine the equivalent discount rate for a period of: i. Six months ii. One year iii. One month
implied interest rate i) r = (1.2/1) ∧(1/4) -1 r = 4.66 ii) r = (1.2/1) ∧(1/2) -1 r= 9.54% iii) r= (1.2/1) ∧(1/24) -1 ????
If you receive $750 at the end of each month for a period of five years. Assuming an interest rate of 6% p.a. a) How much is this equivalent to today? b) How much is this equivalent to at the end of year 5? c) What dollar equivalent would you agree to receive if you preferred to receive all the money at the end of 2.5 years? d) How long would you have to wait to receive the equivalent of $20,000?
"at the end of each month" = 6% = 0.06 = 0.06/12 = 0.005 "five year" = 5x12 = 60 months a) present value of an annuity PVannuity = 750/0.005 x (1-(1/(1.005)⁶⁰)) = 38794.17 b) future value of an annuity FVannuity = 750/0.005 x ((1.005)⁶⁰-1) = 52327.52 c) future value of present cash flow FV= PV x (1+r)∧t FV2.5= 38794.17 x (1.005)³⁰ FV2.5= 45055.55 d) number of payments (ordinary annuity) t=ln(1+((rxFV)/C))/ln(1+r) t= ln(1+((0.005x20,000)/750))/ ln(1.005) t= 25.095
PERPETUITY • The British government has a consol bond outstanding paying £150 p.a. forever. If the current interest rate is 4%: a. What is the value of the bond immediately after a payment is made? b. Part (a) if the payment grows at 1.5% p.a.? c. What is the value of the bond in (a) immediately before a payment is made? d. Part (c) if the payment grows at 2% p.a.?
a) PV = 150/0.04 = $3750 b) PV = 150/(0.04-0.015) = $6000 c) PV = 150 + 150/0.04 = $3900 d) PV = 150 + (150(1.02))/(0.04-0.02) = $7800
1) You can choose between the following options: a) Receive $5,000 today and $5,000 in five years time or b) $13,000 in five years. If you can earn 9.5% p.a., which option do you prefer?
a) PV = 5000/(1.095)⁵ = 3176.138+ 5000 = 8176.138 b) PV = 13000/(1.095)⁵ =8257.96 B.