If the investment period is for 7 years, then A(P) = Pe0.04+7= Pe028 Find a formula for A'(P) Find and interpret A'(8000). a b. c. Compare the approximation to the actual change,
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![You plan to invest in an account which pays 4% compounded continuously.
If the investment period is for 7 years, then A(P) = Pe0.04-7-Pe028 gives the total balance of P dollars.
a Find a formula for A'(P)
Find and interpret A'(8000)
b.
c. Compare the approximation to the actual change..](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1044e98d-537a-4852-ad22-4b965efcb5dc%2Feee5265b-ed57-458b-96ff-6639ff881961%2Fnp0wg_processed.jpeg&w=3840&q=75)
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- To calculate how many years (n) an investment (P) must be kept in an account that earns interest at i%, in order to triple in amount, which of the following expressions should be used? (a) n = -P + F(P/F, i%, n) (b) n = [log (F/P)]/[log (1+ i%)] (c) n = [ In(– P +F)]/[In i%] (d) n = -F(1 + i%)P*Using Matlab* The current amount A of a principal P invested in a savings account paying an annual interest rate r is given by A = P(1+r/n)^(nt) where n is the number of times per year the interest is compounded. For continuous compounding, A = Pe^(rt). Suppose $10,000 is initially invested at 2.5 percent (r = 0.025). a. Plot A versus t for 0 ≤ t ≤ 20 years for four cases: continuous compounding, annual compounding (n = 1), quarterly compounding (n = 4), and monthly compounding (n = 12). Show all four cases on the same subplot and label each curve. On a second subplot, plot the difference between the amount obtained from continuous compounding and the other three cases. b. Redo part a, but plot A versus t on log-log and semilog plots. Which plot gives a straight line?The current amount A of a principal P invested in a savings account paying an annual interest rate r is given by A = P(1+r/n)^(rt) where n is the number of times per year the interest is compounded. For continuous compounding, A = Pe^(rt). Suppose $10,000 is initially invested at 2.5 percent (r = 0.025). a. Plot A versus t for 0 ≤ t ≤ 20 years for four cases: continuous compounding, annual compounding (n = 1), quarterly compounding (n = 4), and monthly compounding (n = 12). Show all four cases on the same subplot and label each curve. On a second subplot, plot the difference between the amount obtained from continuous compounding and the other three cases. b. Redo part a, but plot A versus t on log-log and semilog plots. Which plot gives a straight line?
- Assume that at the beginning of the year, you purchase an investment for $6,300 that pays $130 annual income. Also assume the investment's value has increased to $6,900 by the end of the year. a. What is the rate of return for this investment? Note: Input the amount as a positive value. Enter your answer as a percent rounded to 2 decimal places. Rate of return % b. Is the rate of return a positive or a negative number? Positive NegativeAssume that at the beginning of the year, you purchase an investment for $7,200 that pays $100 annual income. Also assume the investment's value has decreased to $6,800 by the end of the year. (a) What is the rate of return for this investment? (Input the amount as a positive value. Enter your answer as a percent rounded to 2 decimal places.) Rate of return % (b) Is the rate of return a positive or negative number? Positive O NegativeAssume that at the beginning of the year, you purchase an investment for $6,500 that pays $95 annual income. Also assume the investment's value has increased to $7,050 by the end of the year. a. What is the rate of return for this investment? Note: Input the amount as a positive value. Enter your answer as a percent rounded to 2 decimal places.
- b1. F = Pert , which assumes continuous compounding, says that the Future value (F) of an amount (P) invested today at an annual rate (r), expressed as a decimal for the time (t), in years is given by the function. Thus if you invested $100 at the annual rate of 5 1/2% for 6 years and 3 months you would get back (at the end of the time), F = $100e(0.055)(6.25) = $100e(0.3438) = $100(1.4102) = $141.02. If you invest $15000 today, what amount does the formula say you will get back if you leave it for 5 years and 3 months in a savings account paying 4 1/2% annually?Assume the returns from holding an asset are normally distributed. Also assume the average annual return for holding the asset a period of time was 15.3 percent and the standard deviation of this asset for the period was 33.2 percent. Use the NORMDIST function in Excel® to answer the following questions. a. What is the approximate probability that your money will double in value in a single year? (Do not round intermediate calculations and enter your answer as a percent rounded to 3 decimal places, e.g., 32.161.) b. What is the approximate probability that your money will triple in value in a single year? (Do not round intermediate calculations and enter your answer as a percent rounded to 8 decimal places, e.g., 32.16161616.)Average Rate of Return, Cash Payback Period, Net Present Value Method for a Service Company Spanish Peaks Railroad Inc. is considering acquiring equipment at a cost of $288,000. The equipment has an estimated life of 10 years and no residual value. It is expected to provide yearly net cash flows of $36,000. The company's minimum desired rate of return for net present value analysis is 12%. Present Value of an Annuity of $1 at Compound Interest Year 6% 10% 12% 15% 20% 1 0.943 0.909 0.893 0.870 0.833 2 1.833 1.736 1.690 1.626 1.528 3 2.673 2.487 2.402 2.283 2.106 4 3.465 3.170 3.037 2.855 2.589 5 4.212 3.791 3.605 3.353 2.991 6 4.917 4.355 4.111 3.785 3.326 7 5.582 4.868 4.564 4.160 3.605 8 6.210 5.335 4.968 4.487 3.837 9 6.802 5.759 5.328 4.772 4.031 10 7.360 6.145 5.650 5.019 4.192 Compute the following: a. The average rate of return, giving effect to straight-line depreciation on the investment. If required, round your answer to one decimal place. 8 X %
- Assume the returns from holding an asset are normally distributed. Also assume the average annual return for holding the asset a period of time was 16.3 percent and the standard deviation of this asset for the period was 33.5 percent. Use the NORMDIST function in Excel® to answer the following questions. a. What is the approximate probability that your money will double in value in a single year? (Do not round intermediate calculations and enter your answer as a percent rounded to 3 decimal places, e.g., 32.161.) b. What is the approximate probability that your money will triple in value in a single year? (Do not round intermediate calculations and enter your answer as a percent rounded to 8 decimal places, e.g., 32.16161616.) a. b. X Answer is complete but not entirely correct. Probability Probability 0.624 % 0.00000200 X %When an initial amount of P dollars is invested at r% annual interest compounded n times per year, the value of the account (4) after years is given by the equation nt A=P(1 + =)** n Write an equation that represents the value in an account that starts out with an initial investment of $5000 and pays 10% interest compound monthly. Then use that equation to fill the table and use the table to graph the equation. Years (1) Value (4) 0 5 10 15 20 oo → KIAn investment accumulates at a force of interest δt = 0.01t / (3 + 0.01t^2) . Find the present value at time t = 0 of $3,900 due at the end of 7.5 year.
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