Calculus - Applications of Differential Equations

[belowdefeat]

Applications of Differential Equations:

Miranda has saved $20,000 while she was in high school so she can go to university this fall. If the investment earns 9% per year compounded monthly, and she removes $500 each month to pay for living expenses, how much does she have after 3 years of schooling?

I really would appreciate any help getting started!

 

[soroban]

Hello, belowdefeat!

This is not a Differential Equations problem.
It is an application of Geometric Series.

Miranda has saved $20,000 while she was in high school so she can go to university this fall.
If the investment earns 9% per year compounded monthly, and she removes $500 each month to pay for living expenses,
how much does she have after 3 years of schooling?

There is a formula for an amount compounded periodically with a constant periodic withdrawl.

\(\displaystyle A \;=\;P(1+i)^n - A\left[\frac{(1+i)^n-1}{i}\right]\)

. . \(\displaystyle \text{where: }\:\begin{Bmatrix}A &=& \text{Amount in account} \\ P &=& \text{Princial invested} \\ i &=& \text{periodic interest rate} \\ A &=& \text{periodic withdrawl} \\ n &=& \text{number of periods} \end{Bmatrix}\)


\(\displaystyle \text{We are given: }\;\begin{array}{ccccc} P &=& 20,000 \\ i &=& \frac{9\%}{12} &=& 0.0075 \\ A &=& 500 \\ m &=& 36 \end{array}\)


\(\displaystyle \text{Hence: }\:A \;=\;20,000(1.0075)^{36} - 500\left[\frac{1.0075^{36}-1}{0.0075}\right] \;=\;5596.549357\)


\(\displaystyle \text{Therefore, she will have: }\:\$5,596.55\)

 

[belowdefeat]

WOAH. THANKS!!

 

[Deleted member 4993]

Applications of Differential Equations:

Miranda has saved $20,000 while she was in high school so she can go to university this fall. If the investment earns 9% per year compounded monthly, and she removes $500 each month to pay for living expenses, how much does she have after 3 years of schooling?

I really would appreciate any help getting started!

Start with defining unknowns as variables and rates of parameters described in the problem.

Please share with us your work, indicating exactly where you are stuck - so that we may know where to begin to help you.

Soroban's solution does not involve solution of a differential equation - may not be acceptable in your course.