Assuming monthly payment of $250, which implies APR=0.01*12=0.12. If it is different, please specify.
target P=20000, A=250 n=to be determined such that P>=target P=20000 The annuity equation with given (monthly) payment is given by P=250(P/A,i,n) =A((1+i)^n-1)/(i(1+i)^n) =250(1.01^n-1)/(0.01(1.01)^n) =25000(1.01^n-1)/(1.01^n) Solve for n by trial and error, Rewrite 20000<=25000(1-1/1.01^n) => 1.01^n>=25000/20000=1.25 Take log on both sides, n*log(1.01)>=log(5) n>=log(5)/log(1.01)=161. 75 => n=162 (next integer) Check: P=250(P/A,0.01,162)=250*(1.01^162-1)/(.01*1.01^162)=20012.56 ok.
In mathematics, the term "center of dilation" refers to a constant point on a surface from which all other points are either enlarged or compressed. The center of dilation and the scale factor comprise the two properties of a dilation.
