Problem 3.1
For an interest rate of 2% per quarter, determine the nominal interest rate per
(a) semiannual period; (b) year; and (c) 2 years.
Problem 3.2
Identify each of the following interest rate statements as either nominal or effective.
a. 4% per year
b. 6% per year compounded annually
c. 10% per quarter
d. 8% per year compounded monthly
e. 1% per month
f. 1% per month compounded monthly
g. 0.1% per day compounded hourly
h. effective 1.5% per month compounded weekly
i. 12% per year compounded semiannually
j. 1% per month compounded continuously
Problem 3.3
Identify the compounding period associated with each of the following interest rate
statements.
a. 2% per quarter
b. 3% per quarter compounded monthly
c. effective 1% per month compounded weekly
d. nominal 6.5% per year compounded semiannually
e. 1% per month
f. effective 7% per year compounded annually
Problem 3.4
Identify the compounding period for the following interest statements: (a) 3% per year;
(b) 10% per year compounded quarterly; (c) nominal 7.2% per year compounded daily;
(d) effective 3.4% per quarter compounded continuously; and (e) 0.012% per day
compounded hourly.
Problem 3.5
Determine the number of times interest is compounded in 1 year for the following interest
statements: (a) 3% per quarter; (b) 1% per month; and (c) 8% per year compounded
semiannually.
Problem 3.6
Convert an interest rate of 1.5% per month into a nominal interest rate over the following
time periods: (a) quarter; (b) year; (c) semiannual; (d) decade.
Problem 3.7
Convert an interest rate of 2% per quarter compounded monthly into a nominal interest
rate over the following time periods: (a) quarter; (b) 2 months; (c) 2 years; (d) 1 year;
(e) 6 months.
Problem 3.8
For an interest rate of 2% per month, find (a) the effective rate per quarter, and (b) the
effective rate per year.
Problem 3.9
For an interest rate of 12% per year compounded continuously, find (a) the nominal rate
per year, (b) the nominal rate per quarter; (c) the effective rate per quarter, and (d) the
effective rate per month.
Problem 3.10
(a) An interest rate of 6.8% per semiannual period compounded weekly is equivalent to
what weekly interest rate? (b) Is the weekly rate a nominal or effective rate? Assume
26 weeks per 6 months.
Problem 3.11
When interest is compounded monthly and single cash flows are separated by 3 years,
what must the time period be on the interest rate if the value of n in the P/F or F/P
equation is (a) n = 3; (b) n = 6; or (c) n = 12?
Problem 3.12
Deposits of $100 per week are made into an investment account that pays interest of
6% per year compounded quarterly. Identify the payment period, compounding period,
and compounding frequency.
Problem 3.13
A bank advertises quarterly compounding for business checking accounts. What payment
and compounding periods are associated with deposits of daily receipts?
Problem 3.14
Identify the payment period and compounding period for the following situations:
a. Deposits are made each quarter into an account reserved for purchasing new equipment
two years from now. The interest rate on the deposits is 12% per year compounded
monthly.
b. The Williams family takes a $10,000 withdrawal from a second retirement package
each 6 months to pay property and income taxes. The funds are invested in a fixed return
annuity that pays 7% per year.
Problem 3.15
Armstrong Fisheries took out a $400,000 loan. Clyde Armstrong wants to know the
semiannual payment for the next 10 years at the loan interest rate of 8% per year
compounded quarterly.
a. Construct the cash flow diagram and indicate the compounding period and payment
period. What is the compounding frequency for the quoted loan rate?
b. What are the effective interest rate and n value that must be in the (A_P,i%,n) factor to
find the semiannual payment?
Problem 3.16
Assume a problem statement involves only single amounts, that is, no series or gradients,
and the interest rate is stated as 12% per year compounded quarterly. For the following n
values, determine the proper interest rate to use in the factor equations: (a) n = 20
quarters; (b) n = 10 semiannual periods; (c) n = 5 years.
Problem 3.17
A corporation deposits $20 million in a money market account for 1 year. What will be
the difference in the total amount accumulated at the end of the year at 18% per year
compounded monthly versus 18% per year simple interest?
Problem 3.18
The TerraMax truck currently being manufactured and field tested by Oshkosh Truck Co.
is a driverless truck intended for military use. Such a truck would free personnel for non-
driving tasks such as reading maps, scanning for roadside bombs, or scouting for the
enemy. If such trucks would result in reduced injuries to military personnel amounting to
$15 million three years from now, determine the present worth of these benefits at an
interest rate of 10% per year compounded semiannually.
Problem 3.19
Federal facilities associated with an international port of entry at Tornillo, TX, are
expected to cost $54 million. A six-lane, 1274-foot-long bridge is expected to cost
$14 million. Land and inspection facilities, offices, and parking will add another
$10 million to the cost. Construction is expected to take three years. Assuming that all of
the funds are allocated at time 0, what is the future worth of the project in year 3 at an
interest rate of 6% per year compounded quarterly?
Problem 3.20
Crow Corporation, a company that specializes in precision metal fabrication, is
conducting a study to determine if it should update equipment now or later. If the cost
2 years from now is estimated to be $260,000, how much can the company afford to
spend now if its minimum attractive rate of return is 12% per year compounded monthly?
Problem 3.21
Hydrex Mechanical Products plans to set aside $160,000 now for possibly replacing its
large synchronous refiner motors whenever it becomes necessary. The replacement is
expected to take place in 3-1/2 years. Determine how much the company will have in its
investment set-aside account if it achieves a rate of return of 16% per year compounded
quarterly. Find the amount in two different ways using each of the following:
(a) tabulated factors, (b) TVM functions on a calculator, and (c) spreadsheet functions.
Problem 3.22
What is the future worth 4 years from now of a present cost of $242,000 to Hydron, Inc.,
at an interest rate of 18% per year compounded monthly?
Problem 3.23
Soil Mediators, Inc., plans to finance a site reclamation project that will require a 4-year
cleanup period. If the company borrows $4.5 million now and wants to earn 16% per year
compounded semiannually on its investment, how much will the company have to
receive in a lump sum payment when the project is over?
Problem 3.24
A sum of $120,000 now at an interest rate of 10% per year compounded semiannually is
equivalent to how much money 6 years ago? Solve using tabulated factors in two ways:
using the effective annual rate and the effective semiannual rate.
Problem 3.25
Pollution control equipment for a pulverized coal cyclone furnace is expected to cost
$190,000 two years from now and another $120,000 four years from now. If
Monongahela Power wants to set aside enough money now to cover these costs, how
much must be invested at an interest rate of 8% per year compounded quarterly?
Problem 3.26
Periodic outlays for inventory-control software at Baron Chemicals are estimated to be
$120,000 next year, $180,000 in 2 years, and $250,000 in 3 years. What is the present
worth of the costs at an interest rate of 10% per year compounded continuously?
Problem 3.27
For the cash flows shown, determine the future worth in year 5 at an interest rate of 10%
per year compounded continuously. Solve using (a) tabulated factors, and (b) a financial
calculator.
Year 1 2 3 4 5
Cash Flow, $ $300,000 0 $250,000 0 $200,000
Problem 3.28
In order to have enough money to finance his passion for top-level off-road racing, a
mechanical engineer decided to sell some of his “toys.” At time t = 0, he sold his chopper
motorcycle for $18,000. Three months later, he sold his Baja pre-runner SUV for
$26,000. At the end of month six, he got $42,000 for his pro-light race truck. If he
invested all of the money in commodity hedge funds that earned 32% per year
compounded quarterly, how much did he have in the account at the end of 1-1⁄2 years?
Problem 3.29
Head & Shoulders shampoo insured spokesman Troy Polamalu’s (of the Pittsburgh
Steelers) head of hair for $1 million with Lloyd’s of London. The insurance payout
would be triggered if he lost at least 60% of his hair during an on-field event. Assume the
insurance company placed the odds of a payout at 1% in year 5. If Lloyd’s of London
wanted a rate of return of 20% per year compounded semiannually, how much did Head
and Shoulders have to pay in a lump sum amount for the insurance policy?
Problem 3.30
Improvements at a Harley-Davidson Plant are estimated to be $7.8 million. Construction
is expected to take three years. What is the future worth of the project in year 3 at an
interest rate of 6% per year compounded quarterly, assuming the funds are allocated
(a) completely at time 0, and (b) equally at the end of each year?
Problem 3.31
Hemisphere Electric Coop (HEC) is planning to outsource its 51-person information
technology (IT) department to Dyonyx. HEC believes this move will allow it to have
access to cutting edge technologies and skill sets that would be cost prohibitive to build
on its own. If it is assumed that the loaded cost of an IT employee is $100,000 per year,
and that HEC will save 25% of this cost through outsourcing, what is the present worth of
the savings to HEC for a 5-year contract at an interest rate of 0.5% per month? Assume
the same number of contract employees is needed as are currently employed.
Problem 3.32
McMillan Company manufactures electronic flow sensors that are designed as an
alternative to ball-and-tube rotometers. The company recently spent $3 million to
increase the capacity of an existing production line. If the extra revenue generated by the
expansion amounts to $200,000 per month, how long will it take for the company to
recover its investment at an interest rate of 12% per year compounded monthly? Solve
using (a) tabulated factors, and (b) a calculator or spreadsheet.
Problem 3.33
(a) Using tabulated factors for the cash flow series shown, calculate the future worth at
the end of quarter 6 using i = 8% per year compounded quarterly. (b) What are the
calculator functions?
Quarter
0 1 2
3
4 5 6
Cash flow, $
100 100 300
300
300 300 300
Problem 3.34
The by-product department of Iowa Beef has the revenue stream shown. If the interest
rate is an effective 12% per year compounded continuously, determine the annual worth
of the revenues for years 1 through 5.
Year
Revenue, $
0
40,000
1
40,000
2
40,000
3
50,000
4
50,000
5
50,000
Problem 3.35
Video cards based on a high speed data processor typically cost $250. A recently released
light version of the chip costs $150. If Karamba Videos purchases 3000 chips per quarter,
what is the present worth of the savings associated with the cheaper chip over a 2-year
period at an interest rate of 16% per year compounded quarterly?
Problem 3.36
The optical products division of Panasonic is planning a $3.5 million building expansion
for manufacturing its powerful Lumix DMC digital zoom camera. If the company uses an
interest rate of 20% per year compounded quarterly for all new investments, what is the
uniform amount of revenue per quarter the company must realize to recover its
investment in 3 years?
Problem 3.37
Lotus Development has a software rental plan called SmartSuite that is available on the
world wide web. A number of programs are available at $2.99 for 48 hours. If a
construction company uses the service an average of 48 hours per week, what is the
present worth of the rental costs for 10 months at an interest rate of 1% per month
compounded weekly? Assume 4 weeks per month.
Problem 3.38
Bethany Iron and Steel is evaluating possible economic advantages of being involved in
electronic commerce. A modest e-commerce package is available for $30,000. If the
company wants to recover the cost in 2 years, what is the equivalent amount of new
income that must be realized every 6 months at an interest rate of 12% per year
compounded quarterly? Solve using two of the following three approaches: factor
formula, calculator, and spreadsheet.
Problem 3.39
El Paso Water Utilities purchases surface water from Elephant Butte Irrigation District at
a cost of $120,000 per month in the months of February through September. Instead of
paying monthly, the utility makes a single payment of $800,000 at the end of the calendar
year (December) for the water it used. The delayed payment essentially represents a
subsidy by the irrigation district to the water utility. At an interest rate of 0.25% per
month, what is the amount of the subsidy?
Problem 3.40
Phoenix Pump and Filter projects that the cost of steel bodies for Model R910 valves will
increase by $2.50 every 3 months. If the cost for the first quarter is expected to be $90 per
unit, what is the present worth of a unit’s costs over a 3-year time period at an interest
rate of 12% per year compounded quarterly?
Problem 3.41
Spectrum Lab Products, a supplier of high quality lab equipment, borrowed $3 million to
renovate one of its testing labs. The loan was repaid in 2 years through quarterly
payments that increased by $50,000 each time. At an interest rate of 12% per year
compounded quarterly, what was the size of the first quarterly payment? Solve using
(a) tabulated factors, and (b) a spreadsheet and the GOAL SEEK tool.
Problem 3.42
According to a study by the National Association of Colleges and Employers, the average
monthly salary for a recent electrical engineering graduate was $4944 versus $2795 for a
graduate with a degree in liberal arts. What is the future worth in 40 years of the income
difference at an interest rate of 6% per year compounded monthly?
Problem 3.43
Erbitux is a colorectal cancer treatment drug that is manufactured by ImClone Systems,
Inc. If the treatment takes place over a 1 year period at a cost of $10,000 per month and
the patient lives 5 years longer than he/she would have lived without the treatment, how
much would that person have to earn each month beginning 1 month after treatment ends
in order to earn an amount equivalent to the total treatment cost at an interest rate of 12%
per year compounded monthly?
Problem 3.44
Plastics Engineering, Inc., a developer of advanced bolt drive components, recently
began manufacturing sprockets made of polyacetal plastics that are approved for direct
food contact. The company claims that high-precision manufacturing promotes longer
belt life, thereby eliminating costs associated with belt replacement. If Kraft Foods
estimates that maintenance down time costs the company an average of $12,000 per
quarter, how much can the company afford to spend now if the new sprockets would cut
their cost to $2000 per quarter? Assume Kraft Foods uses an interest rate of 12% per year
compounded quarterly and a 2-year cost recovery period.
Problem 3.45
Linear actuators coupled to servo motors are expected to save a pneumatic valve
manufacturer $19,000 per quarter through improved materials handling. If the savings
begin now, what is the future worth of the savings through the end of year 3? The
company uses an interest rate of 12% per year compounded quarterly.
Problem 3.46
An environmental soil cleaning company received a contract to remove BTEX
contamination from an oil company tank farm site. The contract required the soil cleaning
company to provide quarterly invoices for materials and services provided. If the material
costs were $140,000 per quarter and the service charges were calculated as an additional
20% of the material costs, what is the present worth of the contract through the 3-year
treatment period at an interest rate of 1% per month?
Problem 3.47
Redflex Traffic Systems manages red light camera systems that take photographs of
vehicles that run red lights. Red light violations in Hereford County result in fines of $75
per incident. A two-month trial period revealed that the sheriff department could expect
to issue 300 citations per month per intersection. Redflex has proposed installation of
camera systems at 10 intersections. How much could the sheriff department afford to
spend on the project if it wanted to recover the first cost in 2 years at an interest rate of
0.25% per month?
Problem 3.48
Anderson-McKee Construction expects to spend $835,000 for heavy equipment
replacement 2 years from now and another $1.1 million 4 years from now. How much
must the company deposit into a sinking fund each month to provide for the purchases, if
the fund earns at a rate of return of 12% per year compounded monthly? Solve using
(a) tabulated factors, and (b) a calculator.
Problem 3.49
A Hilti PP11 pipe laser can be mounted inside or on top of a pipe, a tripod, or in a
manhole to provide fast and accurate positioning and alignment of pipe sections. Jordon
Construction is building a 23-mile pipeline through the desert to dispose of reverse
osmosis concentrate by injection into a fractured-dolomite formation. The PP11 laser can
reduce construction costs through time savings by $9000 per month. What is the
projected future worth of the savings over 2 years, if they start 1 month from now and the
interest rate is 1% per month?
Problem 3.50
The cost of capturing and storing all CO2 produced by coal-fired electricity generating
plants during the next 200 years has been estimated to be $1.8 trillion. At an interest rate
of 10% per year compounded monthly, what is the equivalent annual worth of such an
undertaking over the 200 years?
Problem 3.51
Rotary encoder collars with targets on the face or outside diameter add speed sensing
capability to rotating shafts. SKF Manufacturing expects sales of $150,000 in quarter
one, increasing by $5,000 per quarter through year 5. Calculate the present worth of the
sales through a 5-year period at an interest rate of nominal 20% per year compounded
quarterly.
Problem 3.52
A company that manufactures brushless dc motors recently added a new product line of
thin beam load cells. Start-up costs over the first 6 months were constant at $48,000 per
month. Due to increased manufacturing efficiency, starting in month 7, costs were
$46,000 and continued to decrease by $2000 per month through the end of the year.
Using an interest rate of 18% per year compounded monthly, calculate the equivalent
monthly cost for the first year. Solve using (a) tabulated factors, and (b) as spreadsheet.
Problem 3.53
For the cash flows shown, determine the future worth in year 5 at an interest rate of 1%
per month.
Year 1 2 3 4 5
Cash Flow, $ 300,000 275,000 250,000 225,000 200,000
Problem 3.54
Receipts from sales of hardened steel connectors was $50,000 in the first quarter, $51,000
in the second, and amounts increasing by $1000 per quarter through year 4. What is the
equivalent uniform amount per quarter if the interest rate is 3% per quarter?
Problem 3.55
Atlas Moving and Storage wants to have enough money to purchase a new tractor-trailer
in 4 years at a cost of $290,000. If the company sets aside $4000 in month 1 and plans to
increase its set aside by a uniform amount each month, how much must the increase be
provided the funds earn 6% per year compounded monthly?
Problem 3.56
Frontier Airlines hedged the cost of jet fuel by purchasing options that allowed the airline
to purchase fuel at a fixed price for 2 years. If the savings in fuel costs were $140,000 in
month 1, $141,400 in month 2, and amounts increasing by 1% per month through the 2-
year option period, what was the present worth of the savings at an interest rate of 18%
per year compounded monthly?
Problem 3.57
Find the present worth of an investment that starts at $8000 in year 1 and increases by
10% each year through year 7, if the interest rate is 10% per year compounded
continuously.
Problem 3.58
Corrosion problems and manufacturing defects rendered a gasoline pipeline between El
Paso and Phoenix subject to longitudinal weld seam failures. Therefore, pressure was
reduced to 80% of the design value. If the reduced pressure results in delivery of less
product valued at $100,000 per month, what will be the value of the lost revenue after a
two-year period at an interest rate of 15% per year compounded continuously.
Problem 3.59
The initial cost of a pulverized coal cyclone furnace is $800,000. If the operating cost is
$90,000 in year 1, $92,700 in year 2, and amounts increasing by 3% each year through a
10-year amortization period, what is the equivalent annual cost of the furnace at an
interest rate of 1% per month?
Problem 3.60
In an effort to save money for early retirement, an environmental engineer plans to
deposit $1200 per month starting one month from now, into a self-directed investment
account that pays 8% per year compounded semiannually. How much will be in the
account at the end of 25 years?
Problem 3.61
If you deposit $1500 per month into a credit union savings account that pays interest at a
rate of 6% per year compounded quarterly, how much will be in the account at the end of
five years? There is no interperiod compounding.
Problem 3.62
There is no interperiod compounding for the transactions shown. Your manager asks you
to determine the amount of money in the account at the end of year 3 at an interest rate of
8% per year compounded semiannually. Draw the cash flow diagram and solve using
(a) tabulated factors, and (b) a spreadsheet.
End of
Quarter
Amount of
Deposit, $
Amount of
Withdrawal, $
1
900
—
2–4
700
—
7
1000
2600
11
—
1000
Problem 3.63
You plan to invest $1000 per month in a stock that pays a dividend at a rate of 4% per
year compounded quarterly. How much will the stock be worth at the end of 9 years if
there is no interperiod compounding?
Problem 3.64
Western Refining purchased a model MTVS peristaltic pump for injecting antiscalant at
its nanofiltration water conditioning plant. The cost of the pump was $1200. If the
chemical cost is $11 per day, determine the equivalent cost per month at an interest rate
of 1% per month. Assume 30 days per month and a 4-year pump life.
Problem 3.65
Income from recycling the paper and cardboard generated in an office building has
averaged $3000 per month for 3 years. What is the future worth of the income at an
interest rate of 8% per year compounded quarterly?
Problem 3.66
Coal-fired power plants emit CO2, which is one of the gases that is of concern with
regard to global warming. A technique that power plants can adopt to keep most of the
CO2 from entering the air is called CO2 capture and storage (CCS). If the incremental
cost of the sequestration process is $0.019 per kilowatt-hour, what is the present worth of
the extra cost over a 3-year period to a manufacturing plant that uses 100,000 kWh of
power per month? The interest rate is 12% per year compounded quarterly.
Problem 3.67
The Autocar E3 refuse truck has an energy recovery system developed by Parker
Hannifin LLC that is expected to reduce fuel consumption by 50%. Pressurized fluid
flows from carbon fiber–reinforced accumulator tanks to two hydrostatic motors that
propel the vehicle forward. The truck recharges the accumulators when it brakes. The
fuel cost for a regular refuse truck is $800 per month. How much can a private waste
hauling company afford to spend on the recovery system, if it wants to recover its
investment in 3 years at an interest rate of 12% per year?
Problem 3.68
Assume you make a single deposit of $1000 into a savings account that pays interest at
0.5% per month. If you want to know how much the account will be worth in 5 years, the
only values you can use for i and n are
a. Effective i per month and n = 60
b. Effective i per quarter and n = 30
c. Effective i per semiannual period and n = 10
d. Either (a) or (c)
Problem 3.69
An interest rate obtained by dividing the nominal rate per year by the number of
compounding periods in that year is
a. A nominal interest rate
b. An effective interest rate
c. An effective interest rate only if the compounding period is monthly
d. Either (b) or (c)
Problem 3.70
If deposits are made monthly into a savings account and you want to know how much
will be in the account after 5 years, the interest rate and n values you have to use are
a. The effective rate per month and n = 60 months
b. The effective rate per quarter and n = 20 quarters
c. The effective rate per year and quarters
d. Either (a), (b) or (c)
Problem 3.71
An interest rate of 2% per month is the same as:
a. 24% per year
b. A nominal 24% per year compounded monthly
c. An effective 24% per year compounded monthly
d. Both (a) and (b)
Problem 3.72
The only time you change the original cash flow diagram in problems involving uniform
series cash flows is when the:
a. payment period is longer than the compounding period
b. payment period is equal to the compounding period
c. payment period is shorter than the compounding period
d. it may be done in any of the cases above, depending upon how the effective interest
rate is calculated
Problem 3.73
Exotic Faucets and Sinks, Ltd. guarantees that their new infra-red sensor faucet will save
any household that has two or more children at least $30 per month in water costs
beginning one month after the faucet is installed. If the faucet is under full warranty for
five years, the minimum amount a family could afford to spend now on such a faucet at
an interest rate of 6% per year compounded monthly is closest to:
a. $149
b. $1552
c. $1787
d. $1890
Problem 3.74
Border Steel invested $800,000 in a new shearing unit. At an interest rate of 12% per year
compounded quarterly, the quarterly income required to recover the investment in 3 years
is closest to:
a. $69,610
b. $75,880
c. $80,370
d. $83,550
Problem 3.75
An engineer analyzing cost data about hydrogen sulfide monitors discovered that the
information for the first three years was missing. However, he knew the cost in year 4
was $1250 and that it increased by 5% each year thereafter. If the same trend applied to
the first three years, the cost in year 1 was:
a. $1312.50
b. $1190.48
c. $1028.38
d. $1079.80
Problem 3.76
A plant manager wants to know the present worth of the maintenance costs for a
reconditioned assembly line. An industrial engineer, who designed the system, estimates
that the maintenance costs are expected to be zero for the first three years, $2000 in year
four, $2500 in year five, and amounts increasing by $500 each year through year 10. At
an interest rate of 8% per year compounded semiannually, the value of n to use in the P/G
equation is:
a. 7
b. 8
c. 10
d. 14
Solution 3.1
(a) Nom i/semi = 0.02*2 = 4%
Solution 3.2
(a) effective;
Solution 3.3
(a) quarter;
Solution 3.4
Solution 3.5
Solution 3.6
Solution 3.7
(a) r = 2% per quarter
Solution 3.8
Solution 3.9
(a) r = 12% per year
Solution 3.10
Solution 3.11
(a) years;
(c) quarter
Solution 3.12
Solution 3.13
Solution 3.14
Solution 3.15
(a) m = 4 times per year
Solution 3.16
(a) Need effective i/quarter: i/quarter = 12%/4 = 3%
Solution 3.17
Solution 3.18
Solution 3.19
In $ million units,
Solution 3.20
Solution 3.21
(a) i = 4% per quarter for n = 4(3.5) = 14 quarters
(b) Calculator functions and results for two methods are:
(c) Spreadsheet functions and results are:
Solution 3.22
Solution 3.23
Solution 3.24
Effective semiannual rate i = 10%/2 = 5% for 12 periods
Solution 3.25
Solution 3.26
Solution 3.27
Solution 3.28
Solution 3.29
Solution 3.30
i/quarter = 6/4 = 1.5% for n = 3(4) = 12 quarters
(b) Cost/year = 7.8 million/3 = $2.6 million
Solution 3.31
Solution 3.32
(a) 3,000,000 = 200,000(P/A,1%,n)
Solution 3.33
(a) F = 100(F/A,2%,7) + 200(F/A,2%,5)
Solution 3.34
First find P; then convert to A
Solution 3.35
Solution 3.36
Solution 3.37
i/week = 0.25%
Solution 3.38
Factor formula: A = 30,000(A/P,6.09%,4)
Solution 3.39
Solution 3.40
Solution 3.41
A = $260,121
(b) Spreadsheet solution with GOAL SEEK
Solution 3.42
Solution 3.43
Find cost of treatments after one year, then monthly equivalent A over 5 years
Solution 3.44
Solution 3.45
= $296,738
Solution 3.46
i/quarter = (1 + 0.01)3 –1 = 3.03%
Solution 3.47
Income/month = 10(75)(300) = $225,000
Solution 3.48
(a) Solve for F at the end of year 4 and then convert to A
Solution 3.49
Solution 3.50
i/year = (1 + 0.00833)12 –1 = 10.47%
Solution 3.51
Solution 3.52
(b)
Solution 3.53
i/year = (1 + 0.01)12 –1 = 12.68%
Solution 3.54
Solution 3.55
Solution 3.56
Find P of geometric gradient at t = 0
Solution 3.57
Solution 3.58
i = e0.0125 – 1 = 1.26% per month
Solution 3.59
Convert all cash flows into present worth P and then find A over 10 years
Solution 3.60
PP < CP. Move monthly deposits to end of 6-month compounding period; find F
Solution 3.61
A/3 months = 3(1500) = $4500
Solution 3.62
Move withdrawals to beginning of periods and deposits to end; find F
Solution 3.63
Solution 3.64
Move chemical cost to end of interest period; find A
Solution 3.65
Move cash flow to end of quarter; find F
Solution 3.66
Move cash flow to end of quarter; find P
Solution 3.67
Move cash flow to end of interest period (year); find P
Solution 3.68
Solution 3.69
Solution 3.70
Solution 3.71
Solution 3.72
Solution 3.73
Solution 3.74
Solution 3.75
Solution 3.76