A loan repayment has an initial balance [MATH]B_0[/MATH] and monthly payments $400, where B(t) is the unpaid balance and
Solution: We can calculate that
I need to find B_0 so that B'(t) is not increasing, or [math]B'(t) <= 0[/math].
But that last expression is always positive (assuming I borrowed a positive amount of money).
B'(t) = 0.02B-400.
What is the most you can borrow without going further into debt each month?Solution: We can calculate that
[MATH]B(t) = B_0e^{0.02t}+20000[/MATH].
I need to find B_0 so that B'(t) is not increasing, or [math]B'(t) <= 0[/math].
[math]B'(t) = 0.02\left(B_0e^{0.02t}+20000\right)-400 = 0.02 B_0e^{0.02t}[/math]
But that last expression is always positive (assuming I borrowed a positive amount of money).