How long will it take an investment earning 2.6% interest annually, compounded monthly, to double

Answer 1

Start with your compound interest formula:

A = P(1+ r/n)^nt

A = final amount, P = starting amount, r = interest rate as a decimal, n = number of times per year interest is compounded, t = years

You are looking for how long it will take, so you will solve for t (years).

Let's say you start with $1 and end with $2 (doubling your money).

r = 0.026 (2.6% as a decimal)

n = 12 ("monthly" represents 12 months in a year)

After substituting in all of your information, you have this:

2 = 1(1+ 0.026/12)^12t

Then you have to simplify

2 = 1.002166666^12t

to solve for a variable in an exponent, you have to use a log like ln()

ln(2) = ln(1.002166666^12t)

When you take the log of something with an exponent, you can move the exponent in front of the natural log.

ln(2) = 12t*ln(1.002166666)

Then divide your 12 and ln(1.002166666)

ln(2)/ (12*ln(1.002166666)) = t

t = 26.69

Your money will double in 26.69 years.

Please let me know if you have any further questions!