# Section 3: Compound Interest

### Instructions

• First, you should watch the concepts videos below explaining the topics in the section.
• Second, you should attempt to solve the exercises and then watch the videos explaining the exercises.
• Last, you should attempt to answer the self-assessment questions to determine how well you learned the material.
• When you have finished the material below, you can start on the next section or return to the main differential equations page.

### Concepts

• Using differential equations to solve problems for compound interest
• Solving compound interest problems when deposits are made at regular intervals

### Exercises

Directions: You should attempt to solve the problems first and then watch the video to see the solution.
1. Suppose we open an IRA at age 25 and make annual investments of $2,000 thereafter in a continuous manner. Suppose the rate of return is 8%. What will be the balance at age 65? $$25,000\left(e^6-1\right) \approx 588,313$$ ### Self-Assessment Questions Directions: The following questions are an assessment of your understanding of the material above. If you are not sure of the answers, you may need to rewatch the videos. 1. Set up an IVP for the amount of balance at $$t$$ year if the initial deposit is$1000 and the annual rate of interest is 2%, and solve it assuming the interest is compounded continuously.
2. What is we continuously withdraw at a rate of \$100 per year in addition to the assumptions of the previous part?