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 

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