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Principles of Engineering Economics with Applications

Zahid A. Khan, Arshad N. Siddiquee, Brajesh Kumar, Mustufa H. Abidi

Chapter 4

Interest Formulae and their Applications - all with Video Answers

Educators

Chapter Questions

01:34

Problem 1

Alphageo Ltd. is considering to procure a new helicopter to ferry its personnel for its drilling operations at Bombay High rig locations. A similar helicopter was purchased 5 years ago at $? 6,50,00,000$. At an interest rate of $8 \%$ per year, what would be the equivalent value as on today of $? 6,50,00,000$ expenditure?

Saad Ali Khan
Saad Ali Khan
Numerade Educator

Problem 2

Hindustan Explorations Ltd. is planning to set aside $? 75,00,000$ for possibly replacing its large gate valves in its oil transportation pipeline network whenever and wherever it becomes necessary. If the rate of return is $21 \%$ and the replacement isn't needed for 5 years from now, how much will the company have in its investment account which it has set-aside?

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02:40

Problem 3

Zylog Systems Ltd. manufactures security systems for industrial and defense applications. It wishes to upgrade the technology for some of its units. It is investigating whether it should upgrade it now or consider upgrading later. If the cost of upgradation as on today is $? 50,00,00,000$ what will be the equivalent investment 4 years later at an interest rate of $9 \%$ ?

Linh Vu
Linh Vu
Numerade Educator
00:22

Problem 4

What is the present worth of a future cost of $? 80,00,000$ to Sriram Piston and Rings Ltd., 7 years from now at a rate of interest of $11 \%$ ?

Amrita Bhasin
Amrita Bhasin
Numerade Educator
01:31

Problem 5

Food Corporation of India wants money to construct a new granary. If the granary will cost $? 2,00,00,000$ to the company, how much should it set aside each year for 5 years if the rate of interest is $10 \%$ per year?

Tanishq Gupta
Tanishq Gupta
Numerade Educator
03:08

Problem 6

Maruti Udyog Ltd, has a budget of $? 7,00,000$ per year to pay for seating system components over the next 8 years. If the company expects the cost of the components to increase uniformly according to an arithmetic gradient of ? 10,000 per year, what would be the cost of the components in year 1 , if the interest rate is $8 \%$ per year?

Saad Ali Khan
Saad Ali Khan
Numerade Educator
02:57

Problem 7

VST Systems, a manufacturer of farm equipment wish to examine its cash flow requirements for the next 7 years. In order to adopt new technology it wishes to replace its manufacturing machines at various times over the next 7 years. It has a plan to invest $? 18,00,000$ two years
from now, $? 25,00,000$ four years from now and $? 65,00,000$ seven years from now. What is the present worth of the planned expenditure at an interest rate of $9 \%$ ?

Nicholas Mogoi
Nicholas Mogoi
Numerade Educator
02:00

Problem 8

A bank employee passed the ICWA examination and his salary was raised by $? 5,000$ starting from the end of year 1. At an interest rate of $6 \%$ per year, what is the present value of $? 5,000$ per year over his remaining 25 years of service?

Priyanka Sadarangani
Priyanka Sadarangani
Numerade Educator
02:57

Problem 9

The Heart Centre, New Delhi wants to purchase an autoclave for its operation theatre (OT). It expects to spend $? 1,20,000$ per year for the OT technician and $? 75,000$ per year for the consumables for the autoclave. At an interest rate of $12 \%$ per year, what is the total equivalent future amount at the end of 5 years?

Nicholas Mogoi
Nicholas Mogoi
Numerade Educator
01:30

Problem 10

Mahindra Renault has signed a contract worth $? 5,00,00,000$ with Motherson Sumi for the supply of electronic control systems of its new upcoming passenger cars. The supply of the systems is to begin after 2 years from now and the payment would be made at the commencement of supply. What would be the present worth of the contract at $15 \%$ per year interest?

Priyanka Sadarangani
Priyanka Sadarangani
Numerade Educator
01:20

Problem 11

Transport Corporation is planning to install GIS systems and temperature loggers in its entire fleet of 1,500 refrigerated trucks for the efficient monitoring during transit. If the installation of such system is expected to reduce the insurance claims by $? 4,50,00,000$ three years from now, how much should the company spend now if it uses an interest rate of $11 \%$ per year?

Nick Johnson
Nick Johnson
Numerade Educator
01:44

Problem 12

Precision Pipes and Profiles uses SS-304 to manufacture flyover railings. It is considering to install a new press in order to reduce its manufacturing cost. If the new press will cost $? 2,20,00,000$ now, how much must the company save each year to recover the investment in 5 years at an interest rate of $15 \%$ per year?

Dale Sanford
Dale Sanford
Numerade Educator
01:31

Problem 13

Innovision Advertising expects to invest $? 35,00,000$ to launch a campaign for a cosmetic product in the first year of its advertising with amount decreasing by $? 2,50,000$ each year subsequently. The company expects an income of $? 1,00,00,000$ in first year increasing by $? 15,00,000$ each year. Determine the equivalent worth in years 1 through 5 of the company's net cash flow at an interest rate of $15 \%$ per year.

Tanishq Gupta
Tanishq Gupta
Numerade Educator
03:08

Problem 14

Mahavir Hanuman Developers expects a revenue of $? 25,00,000$ per year over a period of five years for the development of a real estate site. The expenses involved in the project is $? 10,00,000$ per year. Assume the interest rate of $10 \%$ per year, estimate how much money the company should borrow to finance the project.

Saad Ali Khan
Saad Ali Khan
Numerade Educator
03:37

Problem 15

A savings account was started with an initial deposit of $? 25,000$ in year 1 . If the annual deposits in the account were to increase $10 \%$ each year subsequently, estimate how much money would be in the account over a period of 7 years. Use an interest rate of $6 \%$ per year.

Grant Mansfield
Grant Mansfield
Numerade Educator
02:57

Problem 16

A software professional is planning for her retirement and wishes to invest $12 \%$ of her salary each year into Large Cap Infrastructure Fund. If her current year salary is $? 7,20,000$ and if she expects her salary to increase by $6 \%$ each year, what will be the present worth of the fund after 10 years if it earns $8 \%$ per year?

Nicholas Mogoi
Nicholas Mogoi
Numerade Educator
01:00

Problem 17

Over a period of 12 years, the future worth of a geometric gradient series was found to be $? 10,00,000$. If the rate of interest was $12 \%$ per year and the annual rate of increase was $10 \%$ per year, what was the cash flow amount in year 1 ?

Trinity Steen
Trinity Steen
Numerade Educator
03:12

Problem 18

Over a period of 12 years, the future worth of a geometric gradient series was found to be $? 10,00,000$. If the rate of interest was $12 \%$ per year and the annual rate of increase was $10 \%$ per year, what was the cash flow amount in year 1 ?
$$
\begin{array}{c|c|c|c}
\hline \text { Year } & \text { Expenditures, ? } & \text { Year } & \text { Expenditures, ? } \\
\hline 0 & 0 & 5 & 25,000 \\
\hline 1 & 15,000 & 6 & 25,000 \\
\hline 2 & 15,000 & 7 & 25,000 \\
\hline 3 & 15,000 & 8 & 25,000 \\
\hline 4 & 15,000 & & \\
\hline
\end{array}
$$

Harmender Singh Yadav
Harmender Singh Yadav
Numerade Educator
01:31

Problem 19

Mirza Extrusions, Faridabad produces heavy aluminum sections of $13 \mathrm{~m}$ standard length. The company extrudes 100 extruded lengths at $? 1,50,000$ per length in each of the first 2 years, after which the company expects to extrude 125 lengths at $? 1,75,000$ per length through 7 years. If the company's minimum attractive rate of return is $15 \%$ per year, what is the present worth of the expected income?

Tanishq Gupta
Tanishq Gupta
Numerade Educator
00:59

Problem 20

A doctor decides to set aside money for his newborn son's university education. He estimates that his needs will be ? $3,50,000$ on his 18th, 19th, 20th and 21 st birthdays. If he plans to make uniform deposits starting 4 years from now and continue through year 17 , what should be the size of each deposit, if the rate of interest that the account earns is $9 \%$ per year?

Katelyn Chen
Katelyn Chen
Numerade Educator
02:05

Problem 21

OK-Play wishes to purchase an automatic system for ejecting the die-cast products manufactured at its facility. The use of automated system reduces the production cost by $? 25,00,000$ per year in each of the first 3 years and by $? 45,00,000$ per year in the next 3 years. What is the present worth of the cost savings if the company uses an interest rate of $12 \%$ per year?

Charles Carter
Charles Carter
Numerade Educator
06:27

Problem 22

Calculate the future worth of the following income and expenses, if the interest rate is $10 \%$ per year:
$$
\begin{array}{c|c|c}
\hline \text { Year } & \text { Income, ? } & \text { Expenses, ? } \\
\hline 0 & 5,000 & 3,000 \\
\hline 1-6 & 20,000 & 8,000 \\
\hline 7-12 & 25,000 & 10,000 \\
\hline
\end{array}
$$

Amit Srivastava
Amit Srivastava
Numerade Educator
02:14

Problem 23

Calculate the annual worth in years 1 through 12 of the following series of incomes and expenses. Consider rate of interest to be equal to $10 \%$ per year.
$$
\begin{array}{c|c|c}
\hline \text { Year } & \text { Income, ? } & \text { Expenses, ? } \\
\hline 0 & 5,000 & 3,000 \\
\hline 1-6 & 20,000 & 8,000 \\
\hline 7-12 & 25,000 & 10,000 \\
\hline
\end{array}
$$

Willis James
Willis James
Numerade Educator
01:18

Problem 24

A freelance media person is planning for her retirement 30 years from now. She wishes to invest $? 1,50,000$ every year starting now. If she plans to start withdrawing the money 1 year after she makes her last deposit (i.e. $31^{\text {st }}$ year from now), what uniform amount could she withdraw each year for 40 years, if the account earns $8 \%$ interest per year?

Kratika Bhadauria
Kratika Bhadauria
Numerade Educator
01:30

Problem 25

Toyo Rolls expects to increase its income beyond 5 years through 15 years by making suitable investments. In order to achieve this, it plans to invest $? 25,00,000$ now and $? 75,00,000$ four years from now. If the rate of interest is $10 \%$ per year, how much extra income per year would be needed in years 5 through 15 to recover the investment?

Priyanka Sadarangani
Priyanka Sadarangani
Numerade Educator
01:57

Problem 26

Mangalore Refineries and Petrochemicals Ltd. wishes to introduce Employees Provident Fund Scheme (EPFS) by converting Employees Welfare Scheme (EWS) into EPFS. It has already deposited $? 1,00,00,000$ for each of the five years under EWS corpus. How much should be deposited now in order for the corpus to have $? 18,00,00,000$ three years from now, if the corpus grows at a rate of $18 \%$ per year?

Saad Ali Khan
Saad Ali Khan
Numerade Educator
02:35

Problem 27

Find the value of " $y$ " in the diagram shown below that will make the equivalent present worth of the cash flow equal to $? 50,000$ if the interest rate is $10 \%$ per year.
$$
P=? 50,000
$$

Monica Miller
Monica Miller
Numerade Educator
05:25

Problem 28

Calculate the value of " $y$ " for the cash flows as shown in the table below such that the equivalent total value in 10 years is $? 12,00,000$ with an interest rate of $12 \%$ per year.
$$
\begin{array}{c|c|c|c}
\hline \text { Year } & \text { Cash Flow, ? } & \text { Year } & \text { Cash Flow, ? } \\
\hline 0 & 25,000 & 6 & y \\
\hline 1 & 25,000 & 7 & y \\
\hline 2 & y & 8 & y \\
\hline 3 & y & 9 & 15,000 \\
\hline 4 & y & 10 & 15,000 \\
\hline 5 & y & 11 & 15,000 \\
\hline
\end{array}
$$

Jennifer Stoner
Jennifer Stoner
Numerade Educator
05:25

Problem 28

Calculate the value of " $y$ " for the cash flows as shown in the table below such that the equivalent total value in 10 years is $? 12,00,000$ with an interest rate of $12 \%$ per year.
$$
\begin{array}{c|c|c|c}
\hline \text { Year } & \text { Cash Flow, ? } & \text { Year } & \text { Cash Flow, ? } \\
\hline 0 & 25,000 & 6 & y \\
\hline 1 & 25,000 & 7 & y \\
\hline 2 & y & 8 & y \\
\hline 3 & y & 9 & 15,000 \\
\hline 4 & y & 10 & 15,000 \\
\hline 5 & y & 11 & 15,000 \\
\hline
\end{array}
$$

Jennifer Stoner
Jennifer Stoner
Numerade Educator
07:42

Problem 29

The receipts and disbursements of Gati Logistics are shown in the following table. Estimate the future worth in 10 years at an interest rate of $10 \%$ per year.
$$
\begin{array}{c|c|c|c}
\hline \text { Year } & \text { Cash Flow, ? } & \text { Year } & \text { Cash Flow, ? } \\
\hline 0 & -75,00,000 & 4 & 35,00,000 \\
\hline 1 & 20,00,000 & 5 & -8,00,000 \\
\hline 2 & 22,00,000 & 6 & 50,00,000 \\
\hline 3 & 17,50,000 & 7 & 60,00,000 \\
\hline
\end{array}
$$

Md.Daniyal Arshad
Md.Daniyal Arshad
Numerade Educator
03:09

Problem 30

Satnam Overseas is planning to install a captive power plant. The company expects that the maintenance cost of the power plant will be $? 3,00,000$ per year after the captive power plant is put to service. Beginning 3 years from now, however, the maintenance cost is likely to increase by $5 \%$ per year into a foreseeable future. The estimated cost of commissioning the plant, as of now, is $? 4,00,00,000$. Once the power plant is put to service, the company will not only save on its own consumed power but sale of excess available power would bring $? 18,00,000$ worth of revenue per year. If the company uses a 7-year study period and an interest rate of $12 \%$ per year, determine whether the company should go for the captive power plant.

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
02:14

Problem 31

Find the present worth at time $t=0$ of the following cash flow diagram. Assume rate of interest of $i=10 \%$ per year.

Willis James
Willis James
Numerade Educator
03:52

Problem 32

Determine the future worth in year 8 at $\mathrm{i}=8 \%$ per year for the cash flow diagram shown below:

Narayan Hari
Narayan Hari
Numerade Educator
01:38

Problem 33

Calculate the present worth in year 0 of a lease that requires a payment of $? 1,00,000$ now and amounts increasing by $4 \%$ per year through year 10 . Use an interest rate of $12 \%$ per year.

Gregory Higby
Gregory Higby
Numerade Educator

Problem 34

For the cash flows shown below find the value of " $y$ " that makes the present worth in year 0 equal to $? 5,00,000$ at an interest of $10 \%$ per year.
$$
\begin{array}{c|c|c|c}
\hline \text { Year } & \text { Cash Flow, ? } & \text { Year } & \text { Cash Flow, ? } \\
\hline 0 & 1,000 & 6 & 7,000 \\
\hline 1 & 2,000 & 7 & 8,000 \\
\hline 2 & 3,000 & 8 & 9,000 \\
\hline 3 & 4,000 & 9 & 10,000 \\
\hline 4 & \mathrm{y} & 10 & 11,000 \\
\hline 5 & 6,000 & & \\
\hline
\end{array}
$$

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00:58

Problem 35

A machine has an initial cost of $? 1,50,000$, a life of 10 years, and an annual operating cost of $? 10,000$ for the first 3 years, increasing by $8 \%$ per year thereafter. Use an interest rate of $10 \%$ per year and calculate the present worth for the machine.

AG
Ankit Gupta
Numerade Educator
03:39

Problem 36

Identify the following interest rate statements as either nominal or effective. (a) $2 \%$ per month, (b) $1.5 \%$ per week, compounded weekly, (c) effective $5 \%$ per quarter, compounded monthly, (d) nominal $12 \%$ per year, compounded quarterly and (e) $12 \%$ per year compounded monthly.

Gregory Higby
Gregory Higby
Numerade Educator
01:50

Problem 37

For an interest rate of $10 \%$ per year compounded every two months, determine the nominal interest rate per (a) six months, (b) year, (c) two years and (d) three years.

Hubert Agamasu
Hubert Agamasu
Numerade Educator
01:30

Problem 38

A large BPO organization wants to have $? 2,50,00,000$ available in 5 years to pay perks to its employees. How much money, must the company set aside now in an account that earns interest at a rate of $12 \%$ per year, compounded quarterly?

Julian Wong
Julian Wong
Numerade Educator
04:56

Problem 39

An interest rate of $12 \%$ per year, compounded quarterly is equivalent to what effective interest rate per year?

Aparna Shakti
Aparna Shakti
Numerade Educator
01:14

Problem 40

What compounding period is associated with nominal and effective rates of $20 \%$ and $21.55 \%$ per year respectively?

Sid Wan
Sid Wan
University of Louisville
03:12

Problem 41

For the transactions shown below, determine the amount of money in the account at the end of year 4 if the interest rate is $8 \%$ per year compounded semi-annually. Assume no inter-period compounding.
$$\begin{array}{c|c|c}
\hline \text { End of Quarter } & \begin{array}{c}
\text { Amount of Deposit, } \\
? \text { per Quarter }
\end{array} & \begin{array}{c}
\text { Amount of Withdrawal, } \\
\text { ? per Quarter }
\end{array} \\
\hline 1 & 5,000 & - \\
\hline 2-4 & 4,000 & - \\
\hline 7-10 & 6,000 & 2,500 \\
\hline 11-12 & 7,000 & 1,500 \\
\hline 15 & - & 3,000 \\
\hline
\end{array}$$

Suzana Milea
Suzana Milea
Numerade Educator
03:12

Problem 42

Determine the uniform quarterly series in quarters 0 through 8 that would be equivalent to cash flows shown below at an interest rate of $12 \%$ per year, compounded quarterly.
$$
\begin{array}{c|c}
\hline \text { Quarter } & \text { Cash Flow, ? per Quarter } \\
\hline 1 & \text { ? } 5,000 \\
\hline 2-3 & ? 6,000 \\
\hline 5-8 & ? 7,000 \\
\hline
\end{array}
$$

Suzana Milea
Suzana Milea
Numerade Educator
00:58

Problem 43

A present sum of $? 50,000$ at an interest rate of $10 \%$ per year, compounded quarterly, is equivalent to how much money 5 years ago?

Amy Jiang
Amy Jiang
Numerade Educator
02:08

Problem 44

Steel Authority of India Ltd. is considering to introduce SAP (an MRP system). The SAP is available for $? 2,00,00,000$. If the company wants to recover the cost in 3 years, what is the equivalent amount of new income that must be realized every quarter, with the interest rate is $12 \%$ per year, compounded monthly?

Shahab Ullah
Shahab Ullah
Numerade Educator
01:09

Problem 45

A person deposits $? 5,000$ per month into a savings account that pays interest at a rate of $8 \%$ per year, compounded semi-annually. How much will be in the account at the end of 10 years? Assume no inter-period compounding.

Mitchell Cutler
Mitchell Cutler
Numerade Educator