How long does it take for an amount of money P to double itself if it’s invested at 6% interest compounded 6 times a year?

Answer 1

Hi Sarah,

You want to use the compounding formula A = P[(1 + (r/n)]^(n*t)

A = ending amount

P = initial principal

r = interest rate

n = number of times compounded per year

t = time period (years)

You can select any amounts for the initial and ending amount. Lets use $1 for initial and $2 for ending.

A = 2

P = 1

r = 0.06

n = 6

t = unknown (solve for this)

2 = 1[1 + (.06/6)]^(6t)

2 = 1.01^(6t)

Now we have to use a log to solve for the variable exponent.

log(base1.01)2 = 6t

69.66 = 6t

t = 11.6 years

Hope this helps!