Explanation Given: A person deposits money into an account, which pays 6 % interest compounded continuously, at a rate of $ 1000 per year for 30 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 6 % interest compounded continuously, at a rate of $ 1000 per year for 30 years. We have S ( t ) = 1000 M = 30 r = 0.06 Present value is calculated as Present Value = ∫ 0 30 1000 e − 0.06 t d t = 1000 ∫ 0 30 e − 0.06 t d t Solve the integral using fundamental theorem of calculus and substitution method. Let − 0.06 t = u , − 0.06 d t = d u d t = d u − 0.06 Also, when t = 0 , u = 0 When t = 30 , t = − 1.8 Present Value = 1000 ∫ 0 − 1 To determine (b) To find the amount of money actually deposited in the account. To determine (c) To find the interest earned during the 30 years.

6th Edition

ISBN: 9781119267874

Author: Hughes-Hallett

Publisher: WILEY

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Question

Chapter 6.5, Problem 8P

To determine

(a)

To find the balance in the account at the end of 30 years.

To determine

(b)

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

To determine

(c)

To find the interest earned during the 30 years.

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Chapter 6.5, Problem 7P

Chapter 6.5, Problem 9P

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Chapter 6 Solutions

APPLIED CALCULUS-WILEYPLUS

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