Example 1. Compound interestWhen interest is compounded continuously, the rate ofchange of the amount x of the investment is proportionalto the amount present. In this case, the proportionalityconstant is the annual interest rate r (as a decimal); thatis, dx/dt = rx.(a) If $2000 is invested at 8%, compoundedcontinuously, find an equation for the future value of theinvestment as a function of time t, in years.(b) How long will it take for the investment to double?(c) What will be the future value of this investment after35 years?

Continuous Compounding interest assumes interest is compounded and added back into the balance an…

When interest is compounded continuously, the rate of change of the amount x of the investment is proportional to the amount present. In this case, the proportionality constant is the annual interest rate r (as a decimal); that is, dx/dt (a) If $2000 is invested at 8%, compounded continuously, find an equation for the future value of the investment as a function of time t, in years. (b) How long will it take for the investment to double? (c) What will be the future value of this investment after 35 years? = rX.

When interest is compounded continuously, the rate of change of the amount x of the investment is proportional to the amount present. In this case, the proportionality constant is the annual interest rate r (as a decimal); that is, dx/dt (a) If $2000 is invested at 8%, compounded continuously, find an equation for the future value of the investment as a function of time t, in years. (b) How long will it take for the investment to double? (c) What will be the future value of this investment after 35 years? = rX.

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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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.)
For the following exercise, use the compound interest formula, A(t) = P 1 + r n nt , where money is measured in dollars.After a certain number of years, the value of an investment account is represented by the expression 10,950 1 + 0.03 2 24 . How many years had the account been accumulating interest? yr
3. Future value The principal of the time value of money is probably the single most important concept in financial management. One of the most frequently encountered applications involves the calculation of a future value. The process for converting present values into future values is called four time-value-of-money variables. Which of the following is not one of these variables? O The present value (PV) of the amount invested O The duration of the investment (N) O The interest rate (I) that could be earned by invested funds O The inflation rate indicating the change in average prices This process requires knowledge of the values of three of
The present value of a lump sum future amount: O A. increases as the interest rate decreases. OB. decreases as the time period decreases. OC. is inversely related to the future value. O D. is directly related to the interest rate.
The formula for calculating the discount rate to use in net present value (NPV) calculations is as follows PV = 1+ (1+r)" Where 'r represents: OA. The number of years you are investing B. The initial investment OC. The number of years - stated as a decimal D. The cost of capital stated as a decimal
*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?
An investment is represented by the equation A(t)=10,250(1+ 0.04/12)120 How many years has the account been accumulating interest?
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?
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The effective rate of interest compounded quarterly is given by i(m)/m. What is m? Write your answer as an integer.
If Po is the initial price of the security, P₁ is the price after you hold it for a year, and X represents a direct payment, an asset's rate of return is equal to: rate of return = (P₁ - Po) rate of return = (P₁ - Po) + X rate of return = (P₁-Po) / Po + XPo rate of return = (P₁ - Po)/Po + X

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