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Concept explainers
PERPETUAL NET INCOME STREAMS The present value of a perpetual stream of income that flows continually at the rate of P(t) dollars year is given by the formula
where r is the interest rate compounded continuously. Using this formula, find the present value of a perpetual net income stream that is generated at the rate of
P(t) = 10,000 + 4000t dollars/year.
Hint:
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Chapter 7 Solutions
Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach
- An investment account with an annual interest rateof 7 was opened with an initial deposit of 4,000 Compare the values of the account after 9 yearswhen the interest is compounded annually, quarterly,monthly, and continuously.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_forwardThe formula for the amount A in an investmentaccount with a nominal interest rate r at any timet is given by A(t)=a(e)rt, where a is the amount ofprincipal initially deposited into an account thatcompounds continuously. Prove that the percentageof interest earned to principal at any time t can becalculated with the formula I(t)=ert1.arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage
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