1. two sources of income with equal present valuec C at time 0 provide annual payents in arrears during 10 years. The first product, i.e. Product 1, pays 50,000 - 2,000k, where k is measured in years, and the second product pays a constant annual amount of b. The present vaues are calculated using a force of interest of delta(t) = 0.05 - 0.002t, where t is measured in years.
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two sources of income with equal present valuec C at time 0 provide annual payents in arrears during 10 years. The first product, i.e. Product 1, pays 50,000 - 2,000k, where k is measured in years, and the second product pays a constant annual amount of b. The present vaues are calculated using a force of interest of delta(t) = 0.05 - 0.002t, where t is measured in years.
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- 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?Income received at the rate of R (t) = 2500 - e0.049t dollars per year, which can then be invested at 3.6% (compounded continuously) for 30 years. Make sure you give an answer to each part! a) To the nearest cent, find the total value of the income stream over this time interval. b) To the nearest cent, find the present value of the income stream over this time interval. c) To the nearest cent, find the future value of the income stream over this time interval.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 $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 Negative(a) Find the present and future value of an income stream of $6000 per year for a period of 10 years if the interest rate, compounded continuously, is 2%. Round your answers to two decimal places. Present value = $ Future value $ (b) How much of the future value is from the income stream? How much is from interest? Round your answers to two decimal places. The amount from the income stream is $ The amount from the interest is $Parents wish to have $150,000 available for a child's education. If the child is now 8 years old, how much money must be set aside at 3% compounded semiannually to meet their financial goal when the child is 18? Click the icon to view some finance formulas. The amount that should be set aside is $ (Round up to the nearest dollar.) ...
- A passbook savings account has a rate of 8%. Find the effective annual yield, rounded to the nearest tenth of a percent, if the interest is compounded 1000 times per year. Click the icon to view some finance formulas. The effective annual yield is %. (Round to the nearest tenth as needed.)Attempt History Current Attempt in Progress Wildhorse Inc. is considering modernizing its production facility by investing in new equipment and selling the old equipment. The following information has been collected on this investment: Cost Old Equipment Accumulated depreciation Remaining life Current salvage value Salvage value in 8 years Annual cash operating costs $80,240 $40,300 8 years $9,920 $0 $35,100 Cost New Equipment Estimated useful life Salvage value in 8 years Annual cash operating costs $38,000 8 years $4,800 $29,900 Depreciation is $10,030 per year for the old equipment. The straight-line depreciation method would be used for the new equipment over an eight-year period with salvage value of $4,800.What is the annual percentage yield (APY) for money invested at an annual rate of (A)4.66% compounded monthly? (B)4.67% compounded quarterly? A) What is the annual percentage yield (APY) for money invested at an annual rate of4.66% compounded monthly? The APY is _______ (Type an integer or decimal rounded to three decimal places as needed.) B) What is the annual percentage yield (APY) for money invested at an annual rate of 4.67% compounded quarterly? The APY is _______ (Type an integer or decimal rounded to three decimal places as needed.)
- Q) Suppose a $4400 investment earns 5.6% compounded annually for 6 years. Which statement is true? a. The interest earned in the last year is the same as the interest earned in the first year.b. More interest is earned in the last year than in the first year.c. More interest is earned in the first year than in the last year.d. No interest is earned until the last year.The function f(x) = 600 represents the rate of flow of money in dollars per year. Assume a 10-year period at 4% compounded continuously. Find (A) the present value, and (B) the accumulated amount of money flow at t = 10. (A) The present value is $ (Do not round until the final answer. Then round to the nearest cent as needed.)Two accounts each begin with a deposit of $7000. Both accounts have rates of 6.5%, but one account compounds interest once a year while the other account compounds interest continuously. Make a table that shows the amount in each account and the interest earned after one year, five years, ten years, and 20 years. iClick the icon to view some finance formulas. 1 year 5 years 10 years 20 years Compounded annually Interest $ $ Balance $ $ $ $ $ $ (Round to the nearest dollar as needed.) Compounded continuously Balance Interest $ $