Explanation Given: A person deposits money into an account, which pays 5 % interest compounded continuously, at a rate of $ 1000 per year for 15 years. Formula Used: Present value of income S ( t ) over the time t at interest rate r % compounded continuously for M years is given as Present Value = ∫ 0 M S ( t ) e − r t d t Future value is given as Future Value = Present Value ⋅ e r M Calculation: Given that a person deposits money into an account, which pays 5 % interest compounded continuously, at a rate of $ 1000 per year for 15 years. We have S ( t ) = 1000 M = 15 r = 0.05 Present value is calculated as Present Value = ∫ 0 15 1000 e − 0.05 t d t = 1000 ∫ 0 15 e − 0.05 t d t Solve the integral using fundamental theorem of calculus and substitution method. Let − 0.05 t = u , − 0.05 d t = d u d t = d u − 0.05 Also, when t = 0 , u = 0 When t = 15 , t = − 0.75 Present Value = 1000 ∫ 0 − 0 To determine (b) To find the amount of money actually deposited in the account. To determine (c) A person deposits money into an account, which pays 5 % interest compounded continuously, at a rate of $ 1000 per year for 15 years. Find the interest earned during the 15 years.

Applied Calculus, 6e WileyPLUS + Loose-leaf

6th Edition

ISBN: 9781119408901

Author: Deborah Hughes-Hallett, Andrew M. Gleason, Patti Frazer Lock, Daniel E. Flath

Publisher: Wiley (WileyPLUS Products)

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Question

Chapter 6.5, Problem 7P

To determine

(a)

To find the balance in the account at the end of 15 years.

To determine

(b)

To find the amount of money actually deposited in the account.

To determine

(c)

A person deposits money into an account, which pays 5% interest compounded continuously, at a rate of $1000 per year for 15 years. Find the interest earned during the 15 years.

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Chapter 6.5, Problem 6P

Chapter 6.5, Problem 8P

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Applied Calculus, 6e WileyPLUS + Loose-leaf

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