Suppose that $17,056 is invested at an interest rate of 5.2% per year, compounded continuously. a) Find the exponential function that describes the amount in the account after time t, in years. b) What is the balance after 1 year? 2 years? 5 years? 10 years? c) What is the doubling time? a) The exponential growth function is P(t) = (Type exponential notation with positive exponents. Do not simplify. Use integers or decimals for any numbers in the equation.)

Suppose that $17,056 is invested at an interest rate of 5.2% per year, compounded continuously. a) Find the exponential function that describes the amount in the account after time t, in years. b) What is the balance after 1 year? 2 years? 5 years? 10 years? c) What is the doubling time? a) The exponential growth function is P(t) = (Type exponential notation with positive exponents. Do not simplify. Use integers or decimals for any numbers in the equation.)

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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The value of a bank account collecting interest which is continuously compounded is modeled by the equation: A = Pet where: A is the value of the account at time t P, or the principal, is the value of the initial investment t is time (measured in years) r is the interest rate (written as a decimal) 1. Suppose that $5000 is put into an account with an interest rate of 8% compounded continuously. a) How much will the account be worth after 3 years (exact value) ? b) How much will the account be worth after 3 years (rounded to the nearest cent) ? c) How many years will it take for the value of the account to double? In an exponential model for population growth, the size of a population at time t is rt described by the equation: N(t) = Net where: N is the initial population or the population at t=0 r is the percentage growth rate t = time and can be measured in different units depending on the problem. Note: You don't have to use e and r. It is often possible to find an equivalent form…
Example 1. Compound interest 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 = rx. (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?
The following exponential growth equation is used to calculate a given quantity's growth over a set period of time: F=P(1+r/100)n Match the letters in the equation to the term that it is representing: F P R N A. initial value B. final value C. interest rate D. years
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?
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.) ...
(b) Show that the data are exponential. (Round your answer to three decimal places.) Each successive ratio of new/old is , which shows that the data is exponential. Find an exponential model for the account balance. (Let t be the time in months and B the savings balance in dollars. Round your parameters to three decimal places.) B(t) = (c) What is the monthly interest rate? (Round your answer to one decimal place.) % (d) What is the yearly interest rate? (Round your answer to one decimal place.) %
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.)
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 $ $
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?
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?
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

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