How many years will it take for an initial investment of 20,000 to grow to 70,000? Assume a rate of interest of 13​% compounded continuously?

Answer 1

Maybe before the end of the year, if inflation picks up like some 3rd world countries or pre-Hitler post WW1 Germany. The interest rate reflects the inflation rate. If China succeeds in replacing the US dollar as the world's reserve currency, we'll be there maybe in a couple months, but then 70K may not even be worth 20K today.

IF Congress passes more trillion dollar or quadrillion budgets and the Fed does more quantitative easing, we may all be standing in food lines, 6 feet apart, with WW2 type food rationing.

Meanwhile

the general formula is exponential

P=Ae^rt where A is what you start with, P what you end up with, e= about 2.732 and t = time, r= rate of interest or in general, the growth rate of anything.

70K=20Ke^rt (K= $1000, or you could used any monetary unit such as pesos)

e^rt = 70/20= 3.5

take natural logs of both sides

rt = ln3.5 = 1.252763...

t = 1.252763/r where r= 13%

t = 9.637 years, a little over 9 1/2 years

Answer 2

Here's the formula: fv=p(1+int/c)^(cn)

future value

principal

int

compound

yrs

70000=20000(1+.13/365)^(365*n)=9.639yrs