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1.
The Lexington Property Development Company has a $10,000 note receivable from a
customer due in three years
. How much is the note worth today if the interest rate is
a. 9%?
b. 12% compounded monthly?
c. 8% compounded quarterly?
d. 18% compounded monthly?
e. 7% compounded continuously?
SOLUTION:
PV = FV [PVF
k,n
]
a. PV = $10,000 [PVF
9,3
]
= $10,000 (.7722)
= $7,722
b. PV = $10,000 [PVF
1,36
]
= $10,000 (.6989)
= $6,989
c. PV = $10,000 [PVF
2,12
]
= $10,000 (.7885)
= $7,885
d. PV = $10,000 [PVF
1.5,36
]
= $10,000 (.5851)
= $5,851
e. FV = PV (e
kn
)
$10,000 = PV [e
.07(3)
]
$10,000 = PV [1.2337]
PV = $8,105.70
Future Value of an Amount – Example 6.1 (page 246)
2. What will a deposit of $4,500 left in the bank be worth under the following conditions:
a. Left for nine years at 7% interest?
b. Left for six years at 10% compounded semiannually?
c. Left for five years at 8% compounded quarterly?
d. Left for 10 years at 12% compounded monthly?
SOLUTION:
FV = PV [FVF
k,n
)
a. FV = $4,500 [FVF
7,9
] = $4,500 (1.8385) = $8,273.25
b. FV = $4,500 [FVF
5,12
] = $4,500 (1.7959) = $8,081.55
c.
FV = $4,500 [FVF
2,20
] = $4,500 (1.4859) = $6,686.55
d.
FV = $4,500 [FVF
1,120
] = $4,500 (3.3004) = $14,851.80
Finding the Interest Rate – Example 6.3, (page 250)
3. What interest rates are implied by the following lending arrangements?
a. You borrow $500 and repay $555 in one year.
b. You lend $1,850 and are repaid $2,078.66 in two years.
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View Full Documentc. You lend $750 and are repaid $1,114.46 in five years with quarterly compounding.
d. You borrow $12,500 and repay $21,364.24 in three years under monthly compounding.
(Note: In c and d, be sure to give your answer as the annual nominal rate.)
SOLUTION:
FV = PV [FVF
k,n
]
a. $555 = $500 [FVF
k,1
]
FVF
k,1
= 1.1100
k = 11%
b. $2,078.66 = $1,850.00 [FVF
k,2
]
FVF
k,2
= 1.1236
k = 6%
c. $1,114.46 = $750.00 [FVF
k,20
]
FVF
k,20
= 1.4859
k = 2%
k
nom
= 8%
d. $21,364.24 = $12,500.00 [FVF
k,36
]
FVF
k,36
= 1.7091
k = 1.5%
k
nom
= 18%
Solving for the Number of Periods – Example 6.4 (page 251)
4. How long does it take for the following to happen?
a. $856 grows into $1,122 at 7%.
b. $450 grows into $725.50 at 12% compounded monthly.
c. $5,000 grows into $6724.44 at 10% compounded quarterly.
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 Winter '11
 STEVEJOSEPH

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