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SUM-OF-THE-YEARS’-DIGITS METHOD OF DEPRECIATION One of the methods that the Internal Revenue Service allows for computing depreciation of certain business property is the sum-of-the-years'-digits method. If a property valued at C dollars has an estimated useful life of N years and a salvage value of S dollars, then the amount of depreciation
where
Verify that the sum of the arithmetic progression
If office furniture worth $6000 is to be depreciated by this method over
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Finite Mathematics for the Managerial, Life, and Social Sciences
- SalaryA Colleague of the teacher in Exercise 29, hired at the same time, makes $35,000 in her first year and gets a $1200 raise each year. (a) What is her salary Anin her nth year at this school? (b) Find her salary in her eighth year at this school, and compare it to the salary of the teacher in Exercise 29 in his eighth year.arrow_forwardDrug Concentration When a drug is administered orally, it takes some time before the blood concentration reaches its maximum level. After that time, concentration levels decrease. When 500 milligrams of procainamide is administered orally, one model for a particular patient gives blood concentration C, in milligrams per liter, after t hours as C=2.65(e0.2te2t) What is the maximum blood-level concentration, and when does that level occur?arrow_forwardPopulation Growth There are originally 255 foxes and 104 rabbits on a particular game reserve. The fox population grows at a rate of 33 foxes per year, and the rabbits increase at a rate of 53 rabbits per year. Under these conditions, how long does it take for the number of rabbits to catch up with the number of foxes? How many of each animal will be present at that time?arrow_forward
- Home Equity When you purchase a home by securing a mortgage, the total paid toward the principle is your equity in the home. If your mortgage is for P dollars, and if the term of the mortgage is t months, then your equity E in dollars, after k monthly payments is given by E=P(1+r)k1(1+r)t1 Here r is the monthly interest rate as a decimal, with r=APR/12 Suppose you have a mortgage of 425,000 at an APR of 9% and a term of 30 years. How long does it take for your equity to reach half of the amount of the original mortgage? Round r to four decimal places.arrow_forwardSales Strategy A small business is considering hiring a new sales representative sales rep to market its product in a nearby city. Two pay scales are under consideration. Pay Scale 1 Pay the sales rep a base yearly salary of 10, 000 plus a commission of 8 of total yearly sales. Pay Scale 2 Pay the sales rep a base yearly salary of 13, 000 plus a commission of 6 of total yearly sales. a. For each of the pay scales above, use a formula to express the total yearly earnings for the sales rep as a function of total yearly sales. Be sure to identify clearly what the letters that you use mean. b. What amount of total yearly sales would result in the same total yearly earnings for the sales rep no matter which of the two pay scales is used? c. On the same screen, plot the graphs of the functions you made in part a. Copy the picture onto the paper you turn in. Be sure to label the horizontal and vertical axes, and be sure your picture includes the number you found in part b. d. If you were a sales rep negotiating for the new position, under what conditions would you prefer pay scale 1? Under what conditions would you prefer pay scale 2?arrow_forwardLending Money For a certain loan, the interest I due at the end of a loan period is given by I=Prt, where P is the principal barrowed, r is the yearly interest rate as a decimal, and t is the number of years since the money was barrowed. What interest is accrued if 3 years ago we barrowed 5000 at an interest rate of 5%?arrow_forward
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