How long it takes a 2800 investment to earn $500 interest if it's invested at 7% compounded quarterly. round to the nearest tenth of a year.

P=present value of investment = 2800
i=interest per quarter=0.07/4=0.0175
n=number of quarters money invested (to be calculated)
Interest = P[(1+i)^n-1]=500
2800((1+0.0175)^n-1)=500
(1+0.0175)^n=500/2800+1
take log on both sides
n(log(1.0175)=log(1+500/2800)
n=log(1+500/2800)/log(1.0175)
=9.471 quarters
=37.88 months
=37.9 months [ nearest tenth of a month ]