Explanation Given information: A pensioner has a bank account which has $ 20 , 000 , earning 5 % interest compounded continuously. He uses the account to pay himself an annuity, drawing continuously at a $ 2000 annual rate. Explanation: Let f ( t ) be the balance in the account after t years. Rate of change of y = ( Interest ) × ( Balance ) − ( Annuity ) ⇒ y ' = 0.05 y − 2000 ⇒ y ' = 0.05 ( y − 40000 ) ⇒ d y d t = 0.05 ( y − 40000 ) ⇒ d y ( y − 40000 ) = 0.05 d t Integrating both sides, ∫ d y ( y − 40000 ) = ∫ 0.05 d t ⇒ ln | ( y − 40000 ) | = 0.05 t + C ⇒ ( y − 40000 ) = A e 0.05 t ⇒ y = 40 , 000 + A e 0

12th Edition

ISBN: 9780137590810

Author: Larry J. Goldstein, David C. Lay, David I. Schneider, Nakhle H. Asmar, William Edward Tavernetti

Publisher: PEARSON

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Chapter 10, Problem 27RE

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The time the balance in the account will take to be zero, when a pensioner has a bank account which has $20,000 in deposits and earns 5% interest compounded continuously and uses the account to pay himself an annuity, drawing continuously at a $2000 annual rate.

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The time the balance in the account will take to be zero, when a pensioner has a bank account which has $ 20 , 000 in deposits and earns 5 % interest compounded continuously and uses the account to pay himself an annuity, drawing continuously at a $ 2000 annual rate.

Solution Summary: The author calculates the time the balance in the account will take to be zero, when a pensioner has 20,000 in deposits and earns 5% interest compounded continuously.

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The time the balance in the account will take to be zero, when a pensioner has a bank account which has $20,000 in deposits and earns 5% interest compounded continuously and uses the account to pay himself an annuity, drawing continuously at a $2000 annual rate.

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