____________________________ - it is the analysis and evaluation of the factors that will affect the success of engineering projects to the end that a recommendation be made which will ensure the best use of capital. ____________________________ - it is an economic or a market situation in which only a single seller or producer supplies a commodity or a service. ____________________________ - it is a market situation in which there are so few suppliers of a particular product that one supplier’s actions significantly impact prices and supply. ____________________________ - it is a market condition in which a product is traded freely by buyers and sellers in large numbers without any individual transaction affecting the price. ____________________________ - it is an economic or market situation in which a single consumer or buyer buys a commodity or a service from suppliers. ____________________________ - It is an economic or market situation in which there are many sellers or producers that supplies a commodity or a service to very few consumers. ____________________________ - it is an economic system based on the private ownership of the means of production and distribution of goods, characterized by a free competitive market and motivation by profit. ____________________________ - these are tangible things – things that you can touch – that satisfy human wants. ____________________________ - these are activities that people do for themselves or for other people to satisfy their wants. ____________________________ - products or services that are required to support human life and activities, which will be purchased in somewhat the same quantity even though the price varies considerably. ____________________________ - products or services that are desired by humans and will be purchased if money is available after the required necessities have been obtained. ____________________________ - the quantity of a certain commodity that is bought at a certain price at a given place and time. ____________________________ - the quantity of a certain commodity that is offered for sale at a certain price at a given place and time. ____________________________ - under conditions of perfect competition the price at which a given product will be supplied and purchased is the price that will result in the supply and the demand being equal. ____________________________ - when the use of one of the factors of production is limited, either in increasing cost or by absolute quantity, a point will be reached beyond which an increase in the variable factors will result in a less that proportionate increase in output. Simple Interest - interest on an investment that is calculated once per period, usually annually, on the amount of the capital alone and not on any interest already earned. ____________________________ - a type of simple interest in which interest is calculated as through each month had 30 days. Simple Interest I = Pin F = P + I = P + Pin = P(1 + in) where: I = simple interest P = present worth i = interest per period n = number of interest period Problem No. 1 Determine the ordinary simple interest on P5000 for 9 months and 10 days if the rate of interest is 12%. Problem No. 2 Determine the future worth on the previous problem. Problem No. 3 If P1000 accumulates to P1500 when invested at a simple interest for 3 years, what is the rate of interest? Problem No. 4 Jojo bought a 2nd hand DVD player and then sold it to Rowace at a profit of 40%. Rowace then sold the DVD player to Kat at a profit of 20%. If Kat paid 2856 more than it cost Jojo, how much did Jojo pay for the unit? ____________________________ - it is a type of simple interest in which interest is calculated on the basis of a year with 365 days rather than the conventional 360 days. i = r/365 (for ordinary year) = r/366 (for leap year) I = Pin F = P + I = P + Pin = P(1 + in) where: I = simple interest P = present worth i = interest per period n = number of interest period Problem No. 5 The exact simple interest of P5000 invested from June 21, 1995 to December 25, 1995 is P100. What is the rate of interest? Problem No. 6 Calculate for the exact simple interest on P15,000 for the period from February 12, to August 15, 2004 if the rate of simple interest is 12%. Rate of Discount - is the discount of one unit of principal per unit time π r= 1−π where: r = rate of interest d = rate of discount Problem No. 7 A college freshman borrowed P2000 from a bank for his tuition fee and promised to pay the amount for one year. He received only the amount of P1920 after the bank collected an advance interest of P80. What was the rate of discount? Problem No. 8 Ms. Evilla borrowed money from a bank. She receives from the bank P1340 and promised to pay P1500 at the end of 9 months. Determine the corresponding discount rate or often referred to as the banker’s discount. Nominal Rate of Interest (r) - is defined as the basic annual rate of interest. r = im where: i = interest per period m = number of interest per periods per year m = 1 (annually) = 2 (semi-annually) = 4 (quarterly) = 6 (bi-monthly) = 12 (monthly) = 52 (weekly) = 360 (daily) Effective Rate of Interest (ERI) - is defined as the actual or exact rate of interest earned on the principal during one-year period. π πΈπ πΌ = 1 + π π −1 Problem No. 9 What is the effective rate of interest corresponding to 18% compounded daily? Take 1 year = 360 days. Problem No. 10 What rate of interest compounded annually is the same as the rate of interest of 8% compounded quarterly? Problem No. 11 Which of these gives the lowest effective rate of interest? a. 12.35% compounded annually c. 12.20% compounded quarterly b. 11.90% compounded semi-annually d. 11.60% compounded monthly Compound Interest π π =π 1+ π ππ‘ −π π =πΉ 1+ π −ππ‘ πΉ =π 1+π π =πΉ 1+π Continuously Compounding ππ πΉ = ππ π = πΉπ −ππ Single Payment Present Amount Factor = (1 + i)-n Single Payment Future Amount Factor = (1 + i)n Problem No. 12 A loan for P50000 is to be paid in 3 years at the amount of P65000. What is the effective rate of money? Problem No. 13 An amount of P1000 becomes P1608.44 after 4 years compounded bimonthly. Find the nominal interest. Problem No. 14 How long will it take money to double itself if invested at 5% compounded annually? Problem No. 15 By the condition of a will, the sum of P20000 is left to a girl to be held in trust fund by her guardian until it amounts to P50000. When will the girl receive the money if the fund is invested at 8% compounded quarterly? Problem No. 16 If the nominal interest rate is 5% percent, how much is P3000 worth in 15 years in a continuously compounded account? ____________________________ - is defined as a series of equal payments occurring at equal interval of time. ____________________________ - is a type of annuity where the payments are made at the end of each period beginning from the 1st period. 1+π π−1 πΉ=π΄ π 1− 1+π π=π΄ π −π uniform series compound amount factor = uniform series sinking fund factor = 1+π π −1 π π 1+π π −1 uniform series capital recovery factor = uniform series present worth factor = π 1− 1+π −π 1− 1+π −π π Problem No. 17 What annuity is required over 12 years to equate with a future amount of P20000? Assume I = 6% annually. Problem No. 18 How much money must you invest today in order to withdraw P2000 annually for 10 years if the interest rate is 9%? ____________________________ - is a type of annuity where the payments are made at the beginning of each period starting from the 1st period. 1− 1+π π=π΄ π −π 1+π Problem No. 19 Mr. Ayala borrows P100,000 at 10% effective annual interest. He must pay back the loan over 30 years with uniform monthly payments due on the first day of each month. ____________________________ - is the type of annuity where the first payment is made later than the first or is made several periods after the beginning of the annuity. 1− 1+π π=π΄ π −π 1+π −π Problem No. 20 A person buys a piece of lot for P100,000 down payment and 10 deferred semi-annual payments of P8,000 each, starting three years from now. What is the present value of the investment if the rate of interest is 12% compounded semi-annually? ____________________________ - is a series of disbursements or receipts that increases or decreases in each succeeding period by constant amount. Problem No. 21 The Texas Highway Department expects the cost of maintenance for a particular piece of heavy equipment to be P5000 in year 1, P5500 in year 2 and amounts increasing by P500 through year 10. At an interest rate of 10% per year, the present worth of the maintenance cost is Uniform Geometric Gradient - is a series consisting of end-of-period payments, where each payment increases or decreases by a fixed percentage Problem No. 22 The first year maintenance cost for a new automobile is estimated to be P10,000 and it increases at a uniform rate of 10% per year. Using an 8% interest rate, calculate the present worth of cost of the first 5 years of maintenance. ____________________________ - refers to the present worth of a property that is assumed to last forever. The capitalized cost of any property is the “sum of the first cost and the present costs of perpetual replacement, operation and maintenance”. Case 1: No replacement, only maintenance A CC = FC + i Case 2: No maintenance, only replacement P CC = FC + 1+i n−1 Case 3: With maintenance and replacement A π CC = FC + + π i 1+π −1 Problem No. 23 At 6%, find the capitalized cost of a bridge whose cost is P250M and life is 20 years, if the bridge must be partially rebuilt at a cost of P100M at the end of each 20 years. Problem No. 24 An equipment is purchased for P50,000. If the annual maintenance cost is P1500, determine the capitalized cost of perpetual service with an interest rate of 6%. ____________________________ - is the decrease in the value of physical property due to passage of time. d = annual depreciation C0 = first cost BV = book value before life expectancy (L) n = years before life expectancy (L) SV = salvage value Dn = total depreciation after year n dn = depreciation charge on year n ____________________________ πΆ0 − ππ π= πΏ π π·π = ππ = πΆ0 − ππ πΏ π΅ππ = πΆ0 − π·π Problem No. 25 An engineer bought a machine for P500,000. Other expenses including installation amounted to P30,000. At the end of its estimated useful life of 10 years, the salvage value will be 10% of the first cost. Using straight line method of depreciation a) what is the annual depreciation? b) what is the book value after 5 years? Problem No. 26 A printing equipment costs P 73,500 has a life expectancy of 8 yrs. and has a salvage value of P 3500 at the end of its life. The book value at the end of “x” years is equal to P 38,500. Using straight line method of depreciation, solve for the value of “x”. ____________________________ πΆ0 − ππ π π= 1+π π−1 1+π π−1 π·π = π π Problem No. 27 A broadcasting corporation purchased equipment for P53,000 and paid P1,500 for freight and delivery charges to the job site. The equipment has a normal life of 10 years with a trade-in value of P5,000 against the purchase of new equipment at the end of the life. Using sinking fund method, (assume annual interest of 6%) a) Determine the annual depreciation. b) Determine the total depreciation after 5 years. ____________________________ π =1− πΏ π π΅ππ ππ =1− πΆ0 πΆ0 π΅ππ = πΆ0 1 − π π = πΆ0 ππ = πΆ0 1 − π πΏ ππ = ππΆ0 1 − π π−1 ππ πΆ0 πΰ΅ πΏ Problem No. 28 A VOM has a current selling price of P400. If the selling price is expected to decline at a rate of 10% per annum due to obsolence, a) what will be its selling price after 5 years? b) what will be the salvage value if the life expectancy is 10 years? Problem No. 29 A machine worth P250,000 has an estimated life of 15 years with a book value of P30,000 at the end of the period. a) Determine the rate of depreciation. b) Determine the book value after 10 years. c) Determine the depreciation charge during the 10th year. ____________________________ π΅ππ = πΆ0 2 1− πΏ 2 2 ππ = πΆ0 1 − πΏ πΏ ππ = πΆ0 2 1− πΏ π π−1 πΏ Problem No. 30 An asset has a 1st cost of P22,000, an estimated life of 30 years. Using the double declining balance method, a) Determine the book value after 6 years. b) Determine the depreciation charge during the 6th year. c) What is the salvage value? ____________________________ ππ = πΆ0 − ππ πΏ−π+1 πππ· πΏ πΏ+1 πππ· = 2 π 2πΏ − π + 1 π·π = πΆ0 − ππ 2 πππ· Problem No. 31 An asset is purchased for P120,000. Its estimated economic life is 10 years, after which it will be sold for P12,000. Using SOYD a) find the depreciation charge during the 3rd year. b) find the total depreciation after 3 years ____________________________ - is a certificate of indebtedness of a corporation usually for a period not less than ten years and guaranteed by a mortgage on certain assets of the corporation or its subsidiaries πΉπ π= 1− 1+π π −π +πΆ 1+π where: F = face, or par, value C = redemption or disposal price (often equal to F) r = bond rate per period n = number of periods before redemption i = investment rate per period P= value of the bond n periods before redemption −π Problem No. 32 A man wants to make 14% nominal interest compounded semi-annually on a bond investment. How much should he be willing to pay now for a 12%, P10,000- bond that will mature in 10 years and pays interest semi-annually?
