how long will it take for $ 500 to amount $700 of interested at $8% compounded quarterly?

Answer 1

Pt = Po(1+r)^n.

r = (8% / 4) / 100% = 0.02 = Quarterly
% rate expressed as a decimal.

n = The # of compounding periods.

Pt = $500(1.02)^n = $700.
(1.02)^n = 700 / 500 = 1.40.
n*Log(1.02) = Log(1.40).
n = LOg(1.40) / Log(1.02) = 16.991.

T = 16.991Comp. / 4Comp./yr=4.25 Yrs.