You wish to purchase a house for $120,000 in 12 years. You can invest your
money at 4.5%/a compounded semi-annually for the first 5 years and then you
can get 6%/a compounded semi-annually for the next 7 years
A= p(1+r/n) ^nt = p(1+.045/2)2*5
p(1+.045/2)^2*5 + [p(1+.045/2)^2*5](1-.06/2)^2*7 = 120,000
p = 120,000 / [1+.045/2)^2*5 + (1+.045/2)^2*5(1+.06/2)^2*7] = $38,207.59