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 $5000 in an account earning 6.5% 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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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_forwardWhen a particular amount of money P, called the principal, is invested at the interest rate r and is compounded n times a year, the amount A accumulated after t years is A(t) – P(1+ )". = P(1-+ n Determine the amount of money accumulated after 15 years if $5,000 is invested in an account that pays 10 % interest compounded yearly. Round to the nearest cent.arrow_forwardThe tuition in the school year 2012–2013 at a certain university was $15,000. For the school year 2017–2018, the tuition was $17,850. Find an exponential growth function for tuition T (in dollars) at this university t years after the 2012–2013 school year. (Round your values to four decimal places.) T = Assuming it increases at the same annual rate, use the function to predict the tuition (in dollars) in the 2021–2022 school year. (Round your answer to the nearest integer.) $arrow_forward
- At the beginning of the last decade, a total of 7.2 million passengers took a cruise vacation. The global cruising industry has been growing at approximately 7% per year. Assume that this growth rate continues. Suppose N = (t) gives the number of passengers, in millions, that take a cruise vacation at year t. Answer parts (a), (b), (c), and (d) of the question. Click VERIFY to move to the next part. (a) Report the following. Use the pull-down menu to indicate the units. A0) = Number Click for List (b) If (t) is written in the form a-b’, do you predict the value of b to be greater than 1 or less than 1? O b is greater than 1 O b is less than 1 (c) Complete the boxes below to write a formula which gives N as a function of t, where t is in years. Do not round any values. Since your formula gives N in millions of people, check that it passes through the initial value x = 0, N= 7.2, as opposed to passing through x = 0, y = 7,200,000. N= Number ( Number (d) How many millions of cruise…arrow_forwardThe table gives the population of the United States, in millions, for the years 1900–2010. Use a graphing calculator with exponential regression capability to model the US population since 1900. Use the model to estimate the population in 1925 and to predict the population in the year 2020.arrow_forwardWhen a particular amount of money P, called the principal, is invested at the interest rate r and is compounded n times a year, the amount A accumulated after t years is nt A(t) = P(1+ )" n Determine the amount of money accumulated after 15 years if $1, 000 is invested in an account that pays 10 % interest compounded monthly. Round to the nearest cent.arrow_forward
- 2. Find the exponential function that passes through (0,6) and (3,750).arrow_forwardA young person with no initial capital invests k dollars per year at an annual rate of return r. Assume that investments are made continuously and that the return is compounded continuously. b.If r = 7.5%, determine k so that $1 million will be available for retirement in 40 years.arrow_forward3. Determine the exponential function that passes through the points ( 2, 8) and (-1 1) (3 pts) Chparrow_forward
- A bank features a savings account that has an annual percentage rate of r = 2.2% with interest compounded quarterly. Shannon deposits $10,000 into the account. %3D kt -(1+;)". The account balance can be modeled by the exponential formula A(t) = a| 1 + k where A is account value after t years, a is the principal (starting amount), r is the annual percentage rate, k is the number of times each year that the interest is compounded. (A) What values should be used for a, r, and k? a = r = k = (B) How much money will Shannon have in the account in 10 years? Answer = $ Round answer to the nearest penny. (C) What is the annual percentage yield (APY) for the savings account? (The APY is the actual or effective annual percentage rate which includes all compounding in the year). APY = %. Round answer to 3 decimal places. Get help: Video MacBook Proarrow_forwardAccording to the U.S. Customs and Border Protection Agency, the average airport wait time at Chicago’sO’Hare International airport is 16 minutes for a traveler arrivingduring the hours 7–8 a.m., and 32 minutes for arrival during thehours 4–5 p.m. The wait time is defined as the total processingtime from arrival at the airport until the completion of a passenger’s security screening. Assume the wait time is exponentiallydistributed.a. What is the probability of waiting between 10 and 30 minutesfor a traveler arriving during the 7–8 a.m. hour?b. What is the probability of waiting more than 25 minutes for atraveler arriving during the 7–8 p.m. hour?arrow_forward1 Suppose that $63,000 is invested at 6% interest, compounded quarterly. a) Find the function for the amount to which the investment grows after t years. b) Find the amount of money in the account at t=0, 4, 5, and 10 years. a) The function for the amount to which the investment grows after t years is A(t) = - (Simplify your answer. Type an expression using t as the variable.)arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage