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 earning 6.0% interest compounded continuously. Find the total amount in the account for the following time periods. How does the length of time affect the amount of interest earned?
a. 5 yrb. 10 yrc. 15 yrd. 20 yre. 30 yr
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- 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_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_forwardAn 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_forward
- A 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_forward2) 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_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_forward6. Determine the equation for the following exponential function in the form of f(x)=ab*+ c. Show all your steps. (0, 3) -2 1- (2,0) -3 -2 -1 3 -1- -3- 2.arrow_forwardA savings account deposit of $150 is to earn 6.3% compound continuously. Assuming there are no deposit always draws from the account what will be the balance after five years?arrow_forwardThe population, P, of rabbits in a region is growing according to the exponential relation P = 180(1.02)" , where P is the population and n is the number of years. What is the current rabbit population?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_forwardYour are the finance manager for a company that just had a great year. Last year’s income statement and this year’s expectations indicate that the company has a surplus of cash. You decide to invest $100,000 of this cash in a 5 year CD that compounds monthly. The total amount of the investment after the 5 years is given by: A(r)=100,000(1+ r/12)^60 . where r is the annual interest rate. Assuming that the interest rate is 3% (r = 0.03): 1. What is the total amount of the investment after 5 years?2. How fast is the amount growing with respect to r, in dollars per percent?arrow_forwardSuppose that a chemical reaction proceeds according to the law of growth and decay. If half the substance A has been converted at the end of 10 sec, find when nine-tenths of the substance will have been converted. Use 2 decimal places.arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage