Could someone please check my work

A home buyer can afford To spend no more than $800 / month on Mortgage payments. Suppose that the interest rate is 9%% and That the Term of the Mortgage is 20 years. Assume That interest is compounded continuously and that payments are also made continuously. Then determine The maximum amount that this buyer can afford to borrow. 6 ) P = 800 monthly pyme s ( 20 ) = 0 S(t ) = balance due on loan at time , T payoff in 20 yrs Find SCO) max ant buyer can afford to borrow ds = S'(t ) = rate of change of balance = .09 S(+) - 12P = . 09 5 (t) - 12(800) putting linear 15r-order D.E. in standard form: . . S' CT ) ( . 0 9 ) s (t ) = 1- 9600 integrating factor = M = Spit)at ? e S-.oldt -.09t = e using integrating factor Formula: Re s( t ) = [uq (t ) at S (+ ) = fe. (- 9600) dr = - 9600 -. 095 : It Serdt = 1 K e + c = -9600 e-it + C K= =09 -09 -0it =. Le +c = 106666. 6467 e + C -09 S(+ ) = 106464. 6647 + Cp. 09t pay off Use S(20) = 0 condition to solve for C : 5 ( 20) = 0 = 1066 66.6667 + Ce. 09 (20) 1. 8 0 = 106666.6667 + Ce 7 CE - 106646.6647p- 1.8 - 17631. 88142 Find S(0), ant borrowed ! ( S (0 ) = 10 6 6 6 6. 6 6 67 - 17631. 88142 e . 09 (0 ) = $8 9 034.78 528 1 Soln