SOLUTION: The rule of 72 states that if an investment earns p % interest per year, it will take approximately 72/p years for your money to double. You invest 4000 at 4.3 % interest annua

Question 246251: The rule of 72 states that if an investment earns p % interest per year, it will take approximately 72/p years for your money to double.
You invest 4000 at 4.3 % interest annually.
According to the rule of 72, what is the doubling time, in years, for this investment
Use the doubling time to find a formula for v(t) , the value of your investment at time t v(t)?
According to the doubling time, how much will your investment be worth after 32 years?
Use the compound interest formula to find how much the investment will be worth after 32 years?
You may notice that your two values for the investment's worth after 32 years are different. That is because the doubling time you found with the rule of 72 is only an approximation. If the approximation were better, the two values would be the same
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
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.

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