Explanation Given information: The initial amount deposited in the account is $ 2 , 000 . The annual rate of interest in the saving account is 5 % . Additional deposit in the account is $ 100 per month. Formula used: The solution of initial value problem y ' = r y + k , y 0 = p 0 is y = p 0 + k r e r t − k r . Calculation: The additional deposit per annum is $ 100 ⋅ 12 , i .e . $ 1 , 200 . Let y t denotes the amount after t years. If no deposit and withdrawals are made the then rate of change of y is the product of the constant of proportionality 5 % and y . y ' = 5 % ⋅ y = 5 100 ⋅ y = 0.05 y There is an additional deposit is $ 1 , 200 per annum. So, the rate of change is given by y ' = 0.05 y + 1200 Initially, the amount in account for t = 0 is y 0 = 2000 . We have an initial value problem y ' = 0.05 y + 1200 , y 0 = 2000 Find the solution of y ' = 0

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Chapter 5.4, Problem 2CYU

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To find: The time to reach the balance in the account by $20,000

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Chapter 5.4, Problem 1CYU

Chapter 5.4, Problem 1E

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The time to reach the balance in the account by $ 20 , 000

Solution Summary: The author calculates the time to reach the balance in the account by 20,000.

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