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 ]