For Exercises 11–16, suppose that P dollars in principal is invested at an annual interest rate r. For interest compounded n times per year, the amount
Suppose an investor deposits $15,000 in an account for 8 yr at 5.0% interest. Find the total amount of money in the account for the following compounding options. Compare your answers. How does the number of compound periods per year affect the total investment?
a. Compounded annually
b. Compounded quarterly
c. Compounded monthly
d. Compounded daily
e. Compounded continuously
Want to see the full answer?
Check out a sample textbook solutionChapter 12 Solutions
BEGINNING+INTERM.ALG.(LL) >CUSTOM PKG.<
- An investment account was opened with aninitial deposit of 9,600 and earns 7.4 interest,compounded continuously. How much will theaccount be worth after 15 years?arrow_forwardSuppose an investment account is opened with aninitial deposit of 10,500 earning 6.25 interest,compounded continuously. How much will theaccount be warm after 25 years?arrow_forwardfive thousand dollars is deposited into a savings account that has interest compounded continuously. suppose after 3 years the account has grown to six thousand dollars. A.) find the yearly interest rate r for this savings account B.) how long will it take for the initial balance to doublearrow_forward
- The population, P, of raccoons in a region is modelled by the exponential relation P = Po(2)*/20 , where t is the time in years and Po is the initial population. If there are 300 raccoons in the region today, approximately how many raccoons will there be in six years?arrow_forwardA savings account with an interest rate r, which is compounded n times per year, and begins with P as the principal (initial amount), has the discrete nt compounding formula A (t) = P(1+ )". This is because we multiply the amount by itself plus a small amount, determined by the interest rate, and the account grows each time the compounding occurs. For continuous compounding, we use the formula A (t) Pert, and if we have seen this formula before, we may not have gotten a satisfactory answer as to why we use it, other than some vague notion of "compounding infinity times per year". In this exercise, we'll use Bernoulli's Rule to find the connection. It might be helpful to review the "Indeterminate Powers" section of the video before beginning.arrow_forwardSuppose that P dollars are invested at a nominal interest rate of r compounded continuously. Find an equation for the time it takes the investment to double its value.arrow_forward
- An investment will generate income continuously at the constant rate of $1000 per year for 6 years. If the prevailing annual interest rate remains fixed at 7% compounded continuously, what is the present value of the investment? c tooo.arrow_forwardPresent value is the amount of money that must be invested now at a given rate of interest to produce a given future value. For a 1-year investment, the present value can be calculated using Present value = Future value 1 + r , where r is the yearly interest rate expressed as a decimal. (Thus, if the yearly interest rate is 8%, then 1 + r = 1.08.) If an investment yielding a yearly interest rate of 13% is available, what is the present value of an investment that will be worth $4000 at the end of 1 year? That is, how much must be invested today at 13% in order for the investment to have a value of $4000 at the end of a year? (Round your answer to two decimal places.)arrow_forwardFind the accumulated present value of a continuous stream of income at rate R(t) = $250,000, for time T = 18 years and interest rate k = 2%, compounded continuously. The present value is $. (Round to the nearest dollar as needed.) yoarrow_forward
- 2) The value of a plot of land increases 5% every year. The value is $300,000 now, and the owner wants to sell it when the value is at least $400,000. Shanna writes an exponential function of the form, V (t) = a - &, to model the value, V, of the land in t years. The value of b is (A) 1.005 B 1.05 C) 1.5 and the domain is A 0arrow_forwardThe time t (in years) required for an investment to double with interest compounded continuously depends on the interest In rate r according to the function r(r) = a. If an interest rate of 3.5% is secured, determine the length of time needed for an initial investment to double. Round to 1 decimal place. b. Evaluate 1(0.04), 1(0.06), and r(0.08).arrow_forwardSuppose that you now have $10,000 and that you expect to save an additional $4000 during each year, and all of this is deposited in a bank paying 5 percent interest compounded continuously.Let y(t) be your bank balance (in thousands of dollars) after t years. 1. Use your solution to find your bank balance after 10 years.arrow_forwardarrow_back_iosarrow_forward_ios
- Algebra and Trigonometry (MindTap Course List)AlgebraISBN:9781305071742Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage LearningAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage