Raymond B. answered • 07/15/22
Math, microeconomics or criminal justice
26,000 = 6,000(1+0.08/12)^12t
26/6 = (1.00666...)^12t
13/3= about 4.333 = about (1.00666)^12t
about 220.7=12t
t= 220.7/12 = 18.39 years for 6,000 to become 26,000 at 8% compounded monthly
general formula is
A=P(1+r/n)^nt where r= annual interest rate, n=number of compounding periods per year, t = years. P = starting amount, A = ending amount
if the problem had been continuously compounded the formula changes to
A=Pe^rt, e= about 2.718
26/6 = e^.08t
ln4.333 = .08t
t = ln4.333/.08 = about 18.33
compounding monthly takes slightly longer than continous compounding, but not much more: about 3 weeks longer
18.39>18.33 years
plug in .08 for r, 12 for n, 6,000 for P, 26,000 for A, solve for t for the monthly compounding into A=P(1+r/n)^nt,
then t=18.39 years, approximately
