How lnog will it take for an investment of $1000 to double in value if it earns 5% coumpounded weekly?
P = Po(1+r)^n.
P = 2*1000 = $2,000.
Po = $1,000.
r = (5%/52) / 100% = 0.000962 = Weekly %
rate expressed as a decimal.
n = The # of compounding periods.
P = 1000(1.000962)^n = 2,000.
Divide both sides by 1000:
(1.000962)^n = 2.00
Take Log of both sides:
n*Log(1.000962) = Log(2)
n = Log(2) / Log1.000962 = 720.87.
n=720.87Comp. Periods / 52Comp./yr=13.86
Years.