Question 246251
you invest 4000 at 4.3% interest annually.


according to the doubling formula, it will take you 72/4.3 = 16.74418605 years to double your money to 8000.


formula for doubling your money would be:


d = 72/4.3 = 16.74418605


where d = the doubling time in years.


the formula for d is 72/i% where i% is the annual interest rate expressed as a percent.


the formula for the future value of your investment is expressed by the formula:


v(t) = (2*a*t)/d where a is the present amount of your investment and t is the amount of time of your investment in years and d is the amount of time it takes to double your investment in years.


according to this formula, if d = 16.74418605, and t = 16.74418605, and a = 4000, then:


v(16.74418605) = (2 * 4000 * 16.74418605) / 16.74418605 = 2 * 4000 = 8000


this would be correct since this is where we started from.


if t = 32, then this formula becomes:


v(32) = (2 * 4000 * 32) / 16.74418605) = 256000 / 16.74418605 = 15288.88889


with annual compounding, the amount that you would have after 32 years would be 4000 * (1.043)^32 = 15387.13843


they're close.


note that with annual compounding, the amount that you would have in 16.74418605 years would be:


(4000) * (1.043)^16.74418605 = 8094.981366.


again they're close.