A market analyst has obtained the following prices (in Rands) and quantities (in kg) of three commodities - X, Y and Z - sold by a small business entity during 2018 and the current year. 2018 | Current year Commodity | Price (Rands per kg) | Quantity (kg) | Price (Rands per kg) | Quantity (kg) X | 10 | 100 | 15 | 200 Y | 8 | 150 | 13 | 200 Z | 12 | 80 | 18 | 150 Table 3: Prices and quantities of two commodities.
Added by Rodrigo D.
Close
Step 1
2018 Price Quantity (Rands per kg) (kg) 10 100 8 150 12 80 Currentyear Price Quantity (Rands per kg) (kg) 15 200 13 200 18 150 Show more…
Show all steps
Your feedback will help us improve your experience
Adi S and 54 other Intro Stats / AP Statistics educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
A present asset (defender) has a current market value of $85,000 (year 0 dollars). Estimated market values at the end of the next three years, expressed in year 0 dollars, are MV1=$72,000, MV2=$59,000, MV3=$35,000. The annual expenses (expressed in year 0 dollars) are $17,000 and are expected to increase at 4.2% per year. The before-tax nominal MARR is 12% per year. The best challenger has an economic life of 5 years and its associated EUAC is $43,649. Market values are expected to increase at the rate of inflation which is 4% per year. Based on this information and a before-tax analysis, what are the marginal costs of the defender each year and when should you plan to replace the defender with the challenger? Discrete Compounding; i=12% Single Payment Uniform Series Compound Amount Factor Present Worth Factor Compound Amount Factor Present Worth Factor Sinking Fund Factor Capital Recovery Factor N To Find F Given P F/P To Find P Given F P/F To Find F Given A F/A To Find P Given A P/A To Find A Given F A/F To Find A Given P A/P 1 1.1200 0.8929 1.0000 0.8929 1.0000 1.1200 2 1.2544 0.7972 2.1200 1.6901 0.4717 0.5917 3 1.4049 0.7118 3.3744 2.4018 0.2963 0.4163 4 1.5735 0.6355 4.7793 3.0373 0.2092 0.3292 5 1.7623 0.5674 6.3528 3.6048 0.1574 0.2774 6 1.9738 0.5066 8.1152 4.1114 0.1232 0.2432 7 2.2107 0.4523 10.0890 4.5638 0.0991 0.2191 8 2.4760 0.4039 12.2997 4.9676 0.0813 0.2013 9 2.7731 0.3606 14.7757 5.3282 0.0677 0.1877 10 3.1058 0.3220 17.5487 5.6502 0.0570 0.1770 The AW value for Defender is $ ? The AW value for Challenger is $ ? The defender should?
Sri K.
3. If you deposit a dollars into a bank account with an interest rate of k% per year, the value of your deposit after t years is given by a(1 + k/100)^t. The Rule of 70 states that the time it takes for an investment like this to double is approximately 70 divided by the percent growth rate. For example, if the value of an investment is growing at a rate of 2% per year, then the Rule of 70 predicts that it will take approximately 70/2 = 35 years for the investment to double in value. Your work through the first few parts of this problem will justify why the Rule of 70 works. Since the point of the rule is to be a simple approximation that can be done in your head, your work in this problem shouldn't involve a calculator except perhaps to double-check some basic arithmetic (i.e. addition, subtraction, multiplication, or division). (a) Show that the number of years it takes for your deposit to double in value is given by ln(2)/ln(1 + k/100) ≈ 0.70/ln(1 + k/100). (b) Compute the linear approximation L(x) of ln(1 + x) at x = 0. (c) Suppose that the interest rate is 8% per year. Use your linear approximation from (b) to estimate ln(1.08), the denominator of the formula from (a) when k = 8. Then, apply this estimate to the formula from (a) to approximate how long it takes for the deposit to double. Compare this calculation to the one described by the Rule of 70. (d) Now use your linear approximation from (b) to estimate ln(1 + k/100) for any k (i.e., without picking any value for k). How does this justify the Rule of 70? (e) Compute the quadratic approximation Q(x) of ln(1 + x) at x = 0. (f) Using your formula from (a) and your quadratic approximation from (e), estimate the time it will take for your deposit to double in value if the interest rate is 8% per year.
Adi S.
3. Calculate the total number of compounding periods, n, for each of the following: a) compounded semi-annually for 7 years b) compounded monthly for 5 years c) compounded weekly for 3 years 4. Use the compound interest formula, A = P(1 + i)^n, to find the unknown value: a) A=?, P=$1300, i=0.06, n=20 b) A=$8000, P=?, i=0.05, n=24 5. Use the formula, A = P + I, to determine the amount of interest earned if the principal is $1900 and the amount is $2350. 6. How much would an investment of $800 be worth in 90 days if it earns simple interest of 8.4% per annum. 7. An investment of $2200 earned interest at 9.2% per annum compounded quarterly. How much would the investment be worth in 5 years? 8. A car loan can be taken for 4 years. At an interest rate of 8.4% per annum compounded monthly, the total cost of the car loan would be $34243.70. What is the cost of the car if you pay cash for it today rather than take out the loan? 9. Karen made an investment of $2500, two years ago to go on a trip. She invested the money at 7.2% per annum, compounded semi-annually. Her investment will mature in three years. Dwayne would also like to go on the trip. However, he hasn't started saving yet. How much must he invest today at 9.6% per annum, compounded monthly to have the same amount as Karen will have three years from now?
Umar Sohail Q.
Recommended Textbooks
Elementary Statistics a Step by Step Approach
The Practice of Statistics for AP
Introductory Statistics
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD