Exponential Decay) 4\ The value of a car declines exponentially at 7.5% per year. Find the original value of the car if its value when it was 4 years old was OMR 14816.36. Use this formula: P = Pe(-r.t)

Exponential Decay) 4\ The value of a car declines exponentially at 7.5% per year. Find the original value of the car if its value when it was 4 years old was OMR 14816.36. Use this formula: P = Pe(-r.t)

Essentials Of Investments

11th Edition

ISBN:9781260013924

Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.

Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.

Chapter1: Investments: Background And Issues

Section: Chapter Questions

Problem 1PS

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Waiting periods. Fill in the number of periods for the following table,, using one of the three methods below: In (FV/PV) In (1 + r) a. Use the waiting period formula, n = b. Use the TVM keys from a calculator. c. Use the TVM function in a spreadsheet. Present Value 760.13 Future Value $ 1,585.01 Interest Rate 3% Number of Periods years (Round to the nearest whole number.)
For example, if r = 0.1 then $100 saved at the start of period 1 becomes____ at the start of period 2. The value next period of $1 saved now is the____ of that dollar.
6.A young person with no initial capital invests k dollars per year at an annual rate of return r. Assume that investments are made continuously and that the return is compounded continuously. a.Determine the sum S(t) accumulated at any time t.
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?
Please show working Someone promises to pay you $1,000 in years 5, 10 and 15 for a total of $3,000. Assume your required return is 8%. a. what is the duration of this promise to pay you $3,000 over 15 years? b. what's the convexity? c. using the duration estimate alone, what is the estimated percentage price change in t=0 value if rates are expected to increase 2%?
*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?
6. If the effective interest rate is i per period and you invest b dollars at time 0, then the value at time n is b(1 + i)”. For example, if at time 0 you invest $100 at an effective interest rate of 6% per year, then the value at time 1 is $100(1+0.06) = $106. dollars. At time 2, the value will be $100 (1 + 0.06)² = $112.36. Similarly, the present value (value at time 0) of $100 received 2 years from now would be $100(1+0.06)-²≈ $88.99. Sometimes it's convenient to define d = 1/(1 + i) so that we would have $100(1+i)n = $100d". If the interest rate per year is i compounded semiannually, then the effective annual interest rate is (¹ + 2)²³ - 1₁ 1. For example, if the interest rate is 6% per year compounded semiannually, the effective annual interest rate is 1 + .06 2 2 - 1 ≈ 6.09%. If the interest rate per year is i compounded quarterly, then the effective annual interest rate is 4 (¹ + 4) * - 1 1. (a) If the interest rate is 6% per year compounded quarterly, what is the effective…
3. DETAILS ZILLDIFFEQMODAP11 3.1.010. (b) In how many years will the initial sum deposited have doubled? (Round your answer to the nearest year.) years Need Help? When interest is compounded continuously, the amount of money increases at a rate proportional to the amount S present at time t, that is, ds/dt = rs, where r is the annual rate of interest. (a) Find the amount of money accrued at the end of 7 years when $3000 is deposited in a savings account drawing 5 % annual interest compounded continuously. (Round your answer to the nearest cent.) $ (c) Use a calculator to compare the amount obtained in part (a) with the amount S = 3000 1 + S = $ Read It 7(4) 3000(1+1(0.0575)) (*) MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER that is accrued when interest is compounded quarterly. (Round your answer to the nearest cent.)
You are thinking of buildinga new machine that will save you $5,000 in the first year. The machine will then begin to wear out so that the savings decline at a rate of 1% per year forever. What is the present value of the savings if the interest rate is 6% per year? The present value of the savings is $. (Round to the nearest dollar.) -12.. Ereen Sho 529.00 O Time Remaining: 00:25:34 Next etv DD DIL 80 888 FR F7 F6 F5 F4 esc F2 F3 & 2$ % @ #3 7 8. 2 3 4 P Y U W E R Q
Exponential Decay) 4\ The value of a car declines exponentially at 7.5% per year. Find the original value of the car if its value when it was 4 years old was OMR 14816.36. Use this formula: P = Per.t

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