How do I find the time to double and amount after 10 years?

Question

The intial investment is $1000 and the annual % rate is 2.2%. How do I find the time to double and amount after 10 years?

Answer 1

It will take approximately 31.507 years to double the current amount, and in ten years there will be approximately $1,246.08.

For problems involving interest rates and principal amounts, the formula is A = Pe^rt, where P is the principal, or initial amount, r is the rate of interest per year, and t is the time in years. If we want to see the amount of time it will take to double the current amount, we can set up the equation so that 2A = Ae^(0.022)t knowing that the interest rate is 2.2% compounded continuously. We also do not need to use actual values for A or P because the value will simply cancel out when performing the algebra. After dividing both sides of the equations by A, taking the natural logarithm of both sides of the equation, and then dividing both sides of the resulting equation by the interest rate, we find that t = ln(2) / 0.022, which is approximately 31.507. Thus, it will take 31.507 years to have the current amount be doubled.

In order to find the amount after ten years, we require the initial amount of money, which is $1000. Then, we can plug the necessary values into the formula so that A = (100)e^(0.022)(10) ≈ 1246.08. Therefore, there will be approximately $1246.08 in ten years.