It will take 11.60 years for an amount of money p to double itself if its invested at 6 % interest compounded 2 times a year.
For determine the the value of time, use the formula:
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)
According to question, any amount for the initial and ending amount. Let's use $1 for the initial and $2 for the ending.
Given data:
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
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