Pregunta
We describe a savings account with continuous withdrawals that earns interest compounded continuously. Let
denote the money in the account,
years after it was open. Find the differer
equation and initial condition that
satisfies.
Initial amount
, annual interest rate
, withdrawals at the rate of
per month
equation and initial condition that
Initial amount
Ask by Evans Simmons. in the United States
Mar 23,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
The differential equation for the account balance
is:
with the initial condition:
Solución

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Extra Insights
To model this situation, we start with the differential equation for continuous compounding with continuous withdrawals. The money in the account grows at an interest rate
while simultaneously decreasing due to the withdrawals.
The equation will be of the form:
where
is the total rate of withdrawals per year. The monthly withdrawal amount is $500, so the annual withdrawal rate is
. Therefore, the equation becomes:
The initial condition is defined as the amount in the account when it was opened:

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