What is the difference between compound interest and simple interest? Compound Interest Simple Interest TIME From the graph, you can see that simple interest is an example of [ Choose I From the graph, you can see that compound interest is an example of | Choose | MONEY
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- Continuous Compounding A certain investment is subject to continuous compounding. The value of the investment after t years is given by V=5000e0.05tdollars. a. Make a graph of the value of the investment over the first 20 years. b. Is the graph concave up or concave down? Explain in practical terms what the concavity means.The Rule of 72 This is a continuation of Exercise 14. Financial advisors sometimes use a rule of thumb known as Rule of 72 to get a rough estimate of the time it takes for an investment to double in value. For an investment that is compounded yearly at an interest rate of r%, this rule says it will take about 72/r years for the investment to double. In this calculation, r is the integer interest rate rather than a decimal. Thus, if the interest rate is 8%, we would use 72/8 rather than 72/0.08. For the remainder of this exercise, we will consider an investment that is compounded yearly at an interest rate of 13%. a. According to the Rule 72, how long will it take the investment to double in value? Parts b and c of this exercise will check to see how accurate this estimate is for this particular case. b. Using the answer you got from part a of this exercise, calculate the future value interest factor as defined in Exercise 14. Is it exactly the same as your answer to the part a of Exercise 14? c. If your initial investment was 5000, use your answer from part b to calculate the future value. Did your investment exactly double? Future Value Business and finance texts refer to the value of an investment at a future time as its future value. If an investment of P dollars is compounded yearly at an interest rate of r as a decimal, then the value of the investment after t years is given by FutureValue=P1+rt. In this formula, 1+rt is known as the future value interest factor, so the formula above can be written as FutureValue=PFuturevalueinterestfactor Financial officers normally calculate this or look it up in a table a. What future value interest factor will make an investment double? b. Say you have an investment that is compounded yearly at a rate of 9%. Find the future value interest factor for a 7-year investment. c. Use the results from part b to calculate the 7-year future value if your initial investment is 5000.TOPIC: EXPONENTIAL FUNCTION Choose any permissible value of b and graph the function f(x) = bx. In the same Cartesian Plane, for the same value of b, graph the function f(?)= −bx . QUESTION: Based on your observation, what is the relationship between the graph of the two functions? Using the same value of b that you used in Step 1, choose four (4) different values of k and then graph the function f(x) = bx + k.NOTE: The value of k can be negative and identify the asymptote of each function in this Step. QUESTION: What do you think is the effect of k to the graph of the function Again, using the same value of b, choose four (4) different values of h and then graph the function f(x)= bx-hNOTE: The value of h can be negative. QUESTION: What do you think is the effect of h to the graph of the function? FINAL NOTE: Graph is not necessary, I just need to know the answers to the questions.
- TOPIC: EXPONENTIAL FUNCTION Choose any permissible value of b and graph the function f(x) = bx. In the same Cartesian Plane, for the same value of b, graph the function f(x)= −bx . QUESTION: Based on your observation, what is the relationship between the graph of the two functions? Using the same value of b that you used in Step 1, choose four (4) different values of k and then graph the function f(x) = bx + k.NOTE: The value of k can be negative and identify the asymptote of each function in this Step. QUESTION: What do you think is the effect of k to the graph of the function Again, using the same value of b, choose four (4) different values of h and then graph the function f(x)= bx-hNOTE: The value of h can be negative. QUESTION: What do you think is the effect of h to the graph of the function? FINAL NOTE: Graph is not necessary, I just need to know the answers to the questions.Price Appreciation of Homes What will a $90,000condominium cost 5 years from now if the price appreciationfor condos over that period averages 3% compoundedannually?Chapter functions and graphs
- The graph of the function shown illustrates a certain stock market index for the year 2010. Each tic mark on the horizontal axis represents the first opeining day of the market for that given month. Use the graph to answer the following. a. approximately, how much did the index's value increase over 2010? Approximately $_____was gained. b. approximate the average gain per month. on average, the gain was $_____per month.Which exponential functions is shown in the graph below the graph that will be shown. And select the options that are given for the graph.The line graph shows the cost of inflation. The graph shows subsequent years from 1982, comparing what $10,000 bought in 1982, to what it would buy in the years shown. There are two possible mathematical functions for the data.
- Stretching shrinking and reflection to graph the following functionDetermine whether the statement makes sense or does not make sense, and explain your reasoning : "I use the natural base e when determining how much money I’d have in a bank account that earns compound interestsubject to continuous compounding."Find the present value of the given investment.An investment earns 2% per year and is worth $10,000 after 5 years.