A millionaire wants to set up a trust for her grandchild. She wants to put a lump sum of money into an account earning 10% interest. She'd like her grandchild to be able to withdraw $100 every month for the rest of the child's life. Write a differential equation satisfied by f(t), the amount of money in the account at time $\text { t. }$ Does the equation, $y ^ { \prime } = 0.1 \mathrm { y } - 100$ , accurately describe this situation?

Question

A millionaire wants to set up a trust for her grandchild. She wants to put a lump sum of money into an account earning 10% interest. She'd like her grandchild to be able to withdraw $100 every month for the rest of the child's life. Write a differential equation satisfied by f(t), the amount of money in the account at time

\text { t. }

Does the equation,

y ^ { \prime } = 0.1 \mathrm { y } - 100

, accurately describe this situation?

Quizplus · Accepted Answer

The differential equation $y' = 0.1y - 100$ accurately describes the situation where the change in the account balance over time ($y'$) is equal to the interest earned on the account balance ($0.1y$) minus the constant withdrawal rate ($100$).

A Millionaire Wants to Set Up a Trust for Her t. \text { t. } t.

A Millionaire Wants to Set Up a Trust for Her $\text { t. }$