Question 1104551
the formula to use is f = p * (1 + r) ^ n


f is the future value.
p is the present value.
r is the interest rate per time period.
n is the number of time periods.


your time periods are in semi-annual periods which means 2 time periods per year.


your present value is 20792.
your future value is 2 * 20792.
your interest rate per time period is .07 per year / 2 time periods per year  = .035.
your number of time periods is n.


the formula becomes 2 * 20792 = 20792 * (1.035) ^ n.


divide both sides of this equation by 20792 to get 2 = 1.035 ^ n.


take the log of both sides of this equation to get log(2) = log(1.035 ^ n).


since log(1.035 ^ n) is equal to n * log(1.035), this equation becomes log(2) = n * log(1.035).


divide both sides of this equation by log(1.035) to get log(2) / log(1.035) = n.


solve for n to get n = log(2) / log(1.035) = 20.14879168 time periods.


since there are 2 time periods per year, then it will take 20.14879168 / 2 = 10.07439584 years.


round this to 2 decimal places, and it will take 10.07 years.