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You have $ 3 0 , 0 0 0 for a down payment and borrow $ 3 0 0 , 0 0 0 at an

You have $30,000 for a down payment and borrow $300,000 at an annual interest
rate of 5.4%. 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'm having difficulty solving it.

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