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 $10,000 in an account for 5 yr for which the interest is compounded monthly. Find the total amount of money in the account for the following interest rates. Compare your answers and comment on the effect of interest rate on an investment.
a.
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Beginning and Intermediate Algebra
- 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_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 n 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. Why can we write nt lim,→00 P(1+ )"t P limn¬∞ (1+)™ ? narrow_forward
- 2) An initial investment of $10,000 grows at 11% per year. What function represents the value of the investment after t years? R) - 10,000(1.11) R) - 10,000(1.11) - 10,000(11)' A) – 10,000(0.11)' a. c. b. d.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
- Present 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_forward5. Use the formula for a (1+r)" – 1 geometric sum to show that A, = dollars.arrow_forwardSuppose that an amount of 10,000 dollars is invested at an annual interest rate of r% compounded continuously for t years. Then the balance at the end of t years is given by f(t,r)=10,000e0.01rt. (a) f:(5, 3)= (Round to an integer.) This number means that, when $10,000 is invested for years at an annual interest rate of % compounded monthly, if the time increases by 1 year and the annual interest rate remains constant at % , then the balance in the fund --Select--- v by approximately $ (b) f,(5, 3)= 205 monthly, if the annual interest rate increases by 1 percent and the time remains constant at 30 (Round to an integer.) This number means that, when $10,000 is invested for 50 X years at an annual interest rate of 30 X % compounded x years, then the balance in the fund increases v by approximately $ 205arrow_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 amount that should be set aside is $ (Round up to the nearest dollar.)arrow_forward6) A certain radioactive element has a decay rate of 7 % per day, that is it satisfies the equation: dA = -.07A dt a) Find a function that satisfies the equation if the amount of the element present at t=0 is 800 g. (5) b) How much will be present after 20 days? (2)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