T.3.a.i)

Ten years ago () you owed and you continued to borrow at a rate of
       
additional dollars per year for .
If you put equal to the amount you owe years from years ago, then you get
       .
How much do you owe today?

Answer:

The fundamental formula says
       .
So
       .
In this problem:

Here's a plot:

Ouch. Exponential growth is kicking in.
Today you owe this many dollars:

That's a lot of bread - almost a quarter of a million smackers.
If you keep going on this way, here's how many dollars you'll owe years from now:

Out of sight.

T.3.a.ii)

Get the formula for in part a.i) as the solution of a differential equation.

Answer:

This is the same formula you got in part i).
This is no accident because the fundamental formula says
       
       
       
       .
This is the same as saying
        and .

T.3.b.i)

Ten years ago () you owed and you continued to borrow at a rate of
       
additional dollars per year for .
Fortunately your dowager auntie loved you enough to give you a trust fund that pays you at the rate of per year for life.
Ten years ago you decided to use this trust money to help pay off your debt.
Plot your debt as a function of for .
Do you ever get out of debt?  
How much do you owe today?
What are your prospects years from now?

Answer:

Measure in years with corresponding to years ago.
The fundamental formula says
       .
So
       .
In this problem
       :

Here's a plot:

Your auntie put you into the chips.
Today you owe nothing.
Check out what lurks over the next years:

Remember corresponds to today.

Disaster. If you keep going on this way, here's how many dollars you'll owe ten years from now:

Almost five million dollars.
Better find another rich aunt soon.

T.3.b.ii)

Get the formula for in part b.i) as the solution of a differential equation.

Answer:

Ten years ago () you owed and you continued to borrow at a rate of
        additional dollars per year for .
The trust fund that pays you at the rate of per year for life.

This is the same formula you got in part i).
This is no accident because the fundamental formula says
       
       
       
       .
This is the same as saying
        and .