Let y(t) represent your retirement account balance, in dollars, after t years. Each year the account earns 4% interest, and you deposit 4% of your...

Hello!

As I understand, your current annual income is $38000 at t=0, and probably y(0)=0. Then the annual income after t years is `38000*(1.02)^t.`

For each next year, the retirement account balance y(t+1) becomes `y(t)*1.04+38000*(1.02)^t*1.04.` Therefore the difference y(t+1)-y(t) is equal to `y(t)*0.04+38000*1.04*(1.02)^t.`

The left side is something like y'(t): `(y(t+h)-y(t))/h` for h=1 (year). A year is a discrete variable, so h cannot approach zero.

Thus we obtain the differential equation

`y'(t)=y(t)*0.04+39520*(1.02)^t.`

Comments

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