Problema Solution
In how many years will it take a certain investment to double itself if the interest is compounded annually at 6%?
Answer provided by our tutors
P = is the principal value;
r = 0.06 or 6% interest rate;
m = 2 is the number of compounding periods per year;
t = number of year;
i = r/m = 0.06/2 = 0.03 is the interest rate per period;
n = mt = 2t is the number of compounding periods;
A = 2P is the future value;
A = P(1 + i)^n
2P = P(1 + 0.03)^(2t)
P(1 + 0.03)^(2t) = 2P divide both sides by P
(1.03)^(2t) = 2
by solving we find
t = 11.72 years
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in 11.72 years the investment will double itself.