what is the interest rate necessary for an investment to quadruple after 14 years of continuous compound interest

Answer 1

the underlying formula that you want to use here for continuous compounding interest is

A = P*e^(rt)

for this scenario that means taking

4P = P*e^(r*14)

4 = e^(14r)

ln(4) = 14r

r = ln(4) / 14 = 0.09902

meaning that the required interest rate here is 9.90%

Answer 2

Hello Tia,

The formula for continuous compound interest is: A = P* e^rt where r is the interest rate, P is the initial investment, A is the amount t years later, and t is the time that's gone between your investment and when you withdraw the money (Here, t = 14 years)

If an investment quadruples, it means the amount will be 4 times the original investment: A = 4P

So you can create the equation: 4P = P* e^r*14

Divide both sides by P ---> 4 = e^r*14

Take natural log of both sides: ln(4) = ln(e^r*14) and you get: ln(4) = r*14*ln(e)

Since ln(e) = 1, you have: ln(4) = r*14

Divide both sides by 14 and you have: r = ln(4)/14

That is the exact answer, but you would plug it in a calculator to get a numerical value. Be sure to multiply that answer by 100 to get it as a percent value, since you're asked to find an interest rate.