Statement: Paying down a mortgage: you took a $\$200000$ home mortgage at an annual interest rate of 3%.suppose that the loan is amortized over a period of 30 years and let P(t) denote the amount of money(in thousands of dollars) that you owe on the loan after t years.A reasonable estimate of the rate of change of P is given by $ P'(t)=-4.1107e^{0.03t} $. What is the amount of money owed on the loan after 20 years?
I tried to solve it
$$ \frac{dP}{dt}=-4.1107\cdot e^{0.03t} $$
$$ dP=-4.1107\cdot e^{0.03t}dt $$
$$ \int dP=\int-4.1107\cdot e^{0.03t}dt $$
$$ P=-\frac{4.1107}{.03}\cdot e^{0.03t}+c $$
$$ P=-137.023333\cdot e^{0.03t}+c $$ $$ at~ t=0 ~P=200$$
$$ 200=-137.023333+c $$
$$ c=337.023333 $$
$$ P=-137.023333\cdot e^{0.03t}+337.023333 $$ $$ at~ t=20 $$
$$ P=-137.023333e^{.6}+337.023333 $$
$$ P_{20}\approx 87.35054 \cdot1000 $$
So answer is approximately 87350.54.Am i doing anything wrong ?