Problem

An investor has a savings account that pays 3.5% interest. The investor opens the account with $500 and makes an additional deposit of $500 at the end of each year. Assume the function S(t), which gives the amount in the savings account after t years, satisfies the differential equation

Use Euler's method to estimate the amount in the account at the end of 5, 10, and 25 years, using a step size of 0.1.

Solution

The initial point on the graph of S(t) is (0, 500). Using the applet, we get these values for the account balance:

It is worthwhile to note that total of the $500 deposits come to

for each of the time periods under consideration. Everything above that is interest.