You have $$30,000$ for a down payment and borrow $$300,000$ at an annual interest

rate of $5\mathrm{.}4\%.$ Your plan is to make payments at a monthly rate of $1000(1+$ t$/60),$ where t is the number of months since the loan was made. Assuming that this payment schedule can be maintained, when will the loan be fully paid?

The first payment is made in month $1,$ t $=1.$

Can please help me with solving this?

I think the model I would use would be

dP$/$dt $=$ P$($t$)*$r $-$ M$($t$)$

but I$\text{'}$m having difficulty solving it$.$This is for a differential equations class, so I need to solve it analytically. Please do not solve it numerically.