Note for Engineering Economics - EE by Ankur Kukreti

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Prepared By-: Ankur Kukreti Assistant Professor Shivalik College of Engineering QUESTION BANK Q1. Write down the advantages of Compound Interest over Simple Interest? The advantages of compound interest over simple interest are as follows-: Firstly, in S.I interest is calculated as a percentage of the principal amount whereas in C.I interest is calculated as a percentage of principal and accrued interest giving higher amount at the end of the period. Secondly, return on compound interest is higher as compared to the return on Simple Interest. Thirdly, growth of money in compound interest is rapid as compared to the uniform growth of Simple interest. Fourthly, interest is charged on principal + accumulated interest in compound interest whereas interest is charged on constant principal in simple interest therefore compound interest generates more money. Fifthly, C.I generates a higher amount as compared to that of S.I in same period. The following example will explain the difference between the simple and the compound interest. Example: A person has taken a loan of amount of Rs. 10,000 from a bank for a period of 5 years. Estimate the amount of money, the person will repay to the bank at the end of every year for 5 years for the following cases; a) Considering simple interest rate of 8% per year b) Considering compound interest rate of 8% per year Payment using simple interest Year Amount of interest (Rs.) Total amount owed (Rs.) 1 2 3 4 5 800 800 800 800 800 10,800 11,600 12,400 13,200 14,000 Payment using compound interest Year 1 2 3 4 5 Amount of interest (Rs.) 800.00 864.00 933.12 1007.77 1088.39 Total amount owed (Rs.) 10,800.00 11,664.00 12,597.12 13,604.89 14,693.28 Q2. Write down the advantages of Simple Interest over Compound Interest?

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Though C.I has many advantages over S.I but still S.I is preferred over C.I due to the following reasons-: Firstly, S.I is easier to understand. Secondly, Implementation and calculation of S.I is easier as compared to that of C.I. Finally, S.I is widely used in between relatives and friends whereas C.I is used mainly in business transactions. The following example will explain the difference between the simple and the compound interest. Example: A person has taken a loan of amount of Rs. 10,000 from another for a period of 5 years. Estimate the amount of money, the person will repay to the lender after for 5 years for the following cases; a) Considering simple interest rate of 8% per year b) Considering compound interest rate of 8% per year S.I= PRT/100 S.I=10000*8*5/100 S.I=4000 C.I=P{(1+r/100)n-1} C.I=10000{(1+8/100)5-1} C.I=10000{(1.08)5-1} C.I=10000{1.469-1} C.I=10000*0.469 C.I=4693.28 Q3. Define the following-: Simple Interest Compound Interest Simple interest: The interest is said to be simple, when the interest is charged only on the principal amount for the interest period. No interest is charged on the interest amount accrued during the preceding interest periods. In case of simple interest, the total amount of interest accumulated for a given interest period is simply a product of the principal amount, the rate of interest and the time period. It is given by the following expression. S.I.=PRT/100 Where S.I, = total amount of simple interest P = Principal amount R=rate T=time period. Compound interest: The interest is said to be compound, when the interest for any interest period is charged on principal amount plus the interest amount accrued in all the previous interest periods. Compound interest takes into account the effect of time value of money on both principal as well as on the accrued interest also. The following example will explain the difference between the simple and the compound interest. C.I=P{(1+r/100)n-1} Where C.I, = total amount of compound interest P = Principal amount r=rate n=time period. Q4. If Rs.6000 has been put on interest at 12% p.a. for 2 years. How much Amount is received after 2 years if interest is compounded semi-annually? P=Rs. 6000 r=12% n=2 years

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As interest is compounded Semi-Annually, Therefore-: R=12/2=6% n=2*2=4 C.I=6000{(1+6/100)4-1} C.I=6000{(1+0.06)4-1} C.I=1574.86 Q5. Write a short note on CFD with an example. Cash Flow diagram is a diagrammatic representation of cash inflows and outflows of a company over a time line with fixed time interval. It is a picture of a financial problem that shows all cash inflows and outflows along a time line. A CFD (cash flow diagram) is created by drawing a segmented horizontal line divided into appropriate time units. The time units on the CFD can be months, quarters, years or any other consistent time unit. Advantages-: 1. It is a tool used by accountants and engineers to represent the transaction which will take place over the course of a given project. 2. It may also be used to represent payment schedules for bonds, mortgages and other types of loans. 3. It is also used with a break-even sheet and balance sheet in order to see whether money is being made or lost. 4. It is also used to monitor results of different things. 5. It can help to visualize a problem and to determine if it can be solved by time value of money(TVM) methods. Example-: At time zero 1st time period from today 2nd time period from today 3rd time period from today 4th time period from today a positive cash flow of Rs. 100 a negative cash flow of Rs. 100 a positive cash flow of Rs. 100 a negative cash flow of Rs. 150 a negative cash flow of Rs. 50 (+) __________________________________ (-) 0 1 2 3 4 An example cash flow diagram Q6. What is a trade-off. How to determine the prior between guns and butter with life time example? Trade-off is a situation which leads to the conclusion that- “the cost of one this is what you have to forgo to get it”. There always exists a trade-off between guns and butter. Guns states that the amount of money invested in defense purpose of a country whereas butter states that amount of money invested for feeding purpose of a country. The budget of a country remains constant so the more you invested in defense purpose of country the less you are left for investing in the feeding of a country and the less you invest in defense the more you are left to invest in butter. Q7. What is a trade-off. How will you show that it exists between inflation and unemployment with real life example? Trade-off is the cost of one thing that you have to forgo to get it. Similar situation arises whenever society faces trade-offs and it is interesting to note that the trade-offs what society faces are more complex as compared to case of individuals. The classic trade-off is between “guns and butter” and between “inflation and unemployment”. Opportunity cost-: Cost of one thing in real terms is the alternatives that have to be forgone in order to enjoy it. Trade-off between inflation and unemployment-: Inflation exist when demand for goods and services are higher than the rate of production this causes the firms to raise their prices and also encourages them to increase the quantity of goods and

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services they produce to hire more workers to produce the increased demand in order to do that firms hire more workers to produce those goods and services. More hiring of workers means lower employment in the economy. Q8. Write a short note on time value of money? TIME VALUE OF MONEY:It is the value of money figuring in a given amount of interest and over a given amount of time. It is an important concept in financial management. It can be used to compare investment alternatives and to solve problems involving loans, mortgages, leases, savings and annuities. The time value of money theory states that a dollar that you have in the bank today is worth more than a reliable promise or expectation of receiving a dollar at some future date. You can invest the dollar today and earn a return on that investment, such as interest or dividend payments. Uses-:The theory of time value of money allows calculations of future interest earnings. Calculations involving the time value of money allow people to find and compare the value of future payments. To do this, five figures come into play: interest rate, number of periods or number of times interest or dividend payments are made, payments, present value and future value. Formula involving these figures answers questions such as how much you would have to deposit now to have $10,000 in six years if the interest rate is 7 percent. CONCEPT OF TIME VALUE OF MONEY Money has a time value. The sooner we receive money the better it is. The money you hold today is worth more than in future. This phenomenon is referred to as time preference for money. REASONS FOR TIME PREFERENCE OF MONEY (i) The future is uncertain and involves risk (ii) The present needs are considered as urgent as compared to future needs (iii) Postponing use of money means postponing consumption Q9. What is time preference of money? Write reasons for time preference of money. Time preference of money states that the sooner we receive money the better it is. The money you hold today is worth more than in future. This phenomenon is referred to as time preference for money. REASONS FOR TIME PREFERENCE OF MONEY (i) The future is uncertain and involves risk-: Any person can never be certain of getting cash inflows in future and hence he will like to receive money today instead of waiting for the future. (ii) The present needs are considered as urgent as compared to future needs-: People generally prefer to use their money for satisfying their present needs in buying more food, clothes or better households or another car, then deferring them for future. The present needs are considered urgent as compared to future needs. Moreover, there may also be a fear in one’s mind that he may not be able to use the money in future for illness or death. (iii) Postponing use of money means postponing consumption-:Money has some time value. To convince us to postpone consumption and lend or invest our money, we demand a return over time either in the form of interest or some other form such as a capital gain. This means that a specific amount invested today grows to greater amount in future. Q10. Write short note on techniques of time value of money with example. Time value of money is an important concept in financial management. It can be used to compare investment alternatives and to solve problems involving loans, mortgages, leases, savings and annuities. Let’s say you are offered a choice between receiving a lump sum of money now or 5 years later in future. It is generally best to take the money now, because you will have the opportunity to invest it and make more money over those 5 years in the form of interest. The time value of money is the value of money figuring in a given amount of interest and over a given amount of time. The basic rule of finance states that money today is worth more than money to be received in future. This is because money today helps you to buy whatever you want today. It gives you power in form of purchasing power. Money today can be used for consumption to gain satisfaction Q11. Define annuity and due value of annuity. An annuity is a fixed sum paid at regular intervals of time under certain conditions for e.g. The premium payments of Life insurance company are an annuity. When cash flow occurs at the beginning of each period the annuity is called regular annuity and when the cash flow occurs at the end of each month then it is called as Due value of annuity.