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**Unformatted text preview: **Questions and Problems
BASIC @ Future value: Chuck Tomkovick is planning to invest $25,000 today in a mutual fund that will provide a return of 8 percent each year. What will be the value of the investment in 10 years?
LO 2
Solution: 7 "" ' years ' " ’ " "" "
PV = —$25,000 FVs = ? Amount invested today = PV = $25,000
Return expected from investment = z' = 8%
Duration of investment = n = 10 years Value of investment after 10 years = FVlo FVIO : W x (1 + i)“ = $25,000 x (1.08)10
= $53,973.12 @ Future value: Ted Rogers is investing $7,500 in a bank CD that pays a 6 percent armual interest. How much will the CD be worth at the end of ﬁve years? L02 Solution: 0 5 years l—————-——————l PV = $7,500 FV5 = ? Amount invested today = PV = $7,500
Return expected from investment = i = 6%
Duration of investment = n = 5 years
Value of investment after 5 years = FV5 FVS = PV x (1 + i)“ = $7,500 x (1.06)5
= $10,036.69 Future value: Your aunt is planning to invest in a bank deposit that will pay 7.5 percent interest semiannually. If she has $5,000 to invest, how much will she have at the end of four years?
L0 2 in
Solution:
0 4 years
PV=$5000 FV4=~ Amount invested today = PV = $5,000
Return expected from investment = i = 7.5%
Duration of investment = n = 4 years
Frequency of compounding = m = 2 Value of investment after 4 years = FV4 FV4 =PVx(l+——l—) =$5,000x(1+
m 0.075)“ = $5, 000 x (1.0375)8
= $6,712.35 Value of investment after 5 years = FV5 FV5 = PV xe‘" = $100,000 x e
= $100,000 X 1.5488303 = $154,883.03 0.0875x5 5.8 Growth rates: Joe Mauer, a catcher for the Minnesota Twins, is expected to hit 15 home
runs in 2012. If his home run hitting ability is expected to grow by 12 percent every year for the next ﬁve years, how many home runs is he expected to hit in 2017? L04 Solution: ‘
0 5 years
PV = -15 FV5 = ? Number ofhorne runs hit in 2012 = PVrré‘15w H " "7' r N 7 Expected annual increase in home runs hit = i = 12%
Growth period = n = 5 years
Expected home runs in 2017 = FV5 FV5 =PV><(1+g)“ =15><(1.12)5
= 26.4 w 26 home runs Present value: Roy Gross is conSidering an investment that pays 7.6 percent. How much will he have to invest today so that the investment will be worth $25,000 in six years? L03 Solution:
0 6 years +—————————| PV = ? FV6 = $25,000 Value of investment after 6 years = FV5 = $25,000
Return expected from investment = i = 7.6%
Duration of investment = n = 6 years Amount to be invested today = PV W: FVn = $25,000
(1+i)“ (1.076)
=$16,108.92 5.10} Present value: Maria Addai has been offered a future payment of $750 two years from L03 now. If she can earn 6.5 percent compounded annually on her investment, what should she pay for this investment today? 5.11 L03 -X '0 t. _. ' t J .; , 2.;years ' " ' 3"" " r p ' we"— ' ~ ~ ﬂ PV = ? FV2 = $750 Value of investment after 2 years = FVz = $750
Return expected from investment = i = 6.5%
Duration of investment = n = 2 years Amount to be invested today = PV W: FVnn: $7502
(1+i) (1.065)
=$661.24 Present value: Your brother has asked you for a loan and has promised to pay back
$7,750 at the end of three years. If you normally invest to earn 6 percent per year, how much will you be willing to lend to your brother? Solution: 0 3 years
PV = ? FVg = $7,750 Loan repayment amount after 3 years = FV3 = $7,750
Return expected from investment = i = 6%
Duration of investment = n = 3 years Amount to be invested today = PV PVZ FVn :$7,75(3)
(1+z')“ (1.06)
=$6,507.05 32/ Present value: Tracy Chapman is saving to buy a house in ﬁve years. time. She plans to , 7 7,{ ,V, the down payment. If Tracy can invest in a fund that pays 9.25 percent annually, how much will she need to invest today? L03 Solution: 0 5 years PV = ? FV5 = $35,000 Amount needed for down payment after 5 years = FV5 = $35,000
Return expected from investment = z' = 9.25%
Duration of investment = n = 5 years Amount to be invested today = PV _: .wputsdovVnLZOpercent down at ‘tlﬁf tiinfefandtshetb‘e‘lieves,.that.she:wil1%neede$3ég000:fer;..___ s, r_:;.: ,. .. Pv: FVn : $310005
(1+i)” (1.0925) = $22,488.52 5.13 Present value: You want to buy some bonds that will have a value of $1 ,000 at the end of seven years. The bonds pay 4.5 percent interest annually. How much should you pay for them today?
L03
Solution:
0 7 years
PV = ? . FV7 = $1,000 .1; _:,..__r,,Faceivalue of.boﬁd:at:maturityfr:—. EY7‘€$1;000; .. ..._ q: .. , . Appropriate discount rate = i = 4.5%
Number of years to maturity = n = 7 years.
Present value of bond = PV W: FVn : $1,0007
(1+z')n (1.045)
=$734.83 5.14 Present value: Elizabeth Sweeney wants to accumulate $12,000 by the end of 12 years. If the annual interest rate is 7 percent, how much will she have to invest today to achieve her goal?
L03
Solution:
0 12 years ? FV12 = ll PV ...

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- Fall '14
- Garrett
- Future Value