Problema Solution
If $8,000 is placed in an account with an annual interest rate of 6%, how long will it take the amount to quadruple if the interest is compounded annually? Round your answer to two decimal places.
Answer provided by our tutors
Let
P = $8,000 is the principal
A = 4P is the future value after t year
t = the number of years
m = 1 the number of compounding periods per year
n = m*t = t the number of compounding periods
r= 0.06 or 6% the annual interest rate
A = P(1 + r)^n
4P = P(1 + 0.06)^t
P(1 + 0.06)^t = 4P divide both sides by P
(1 + 0.06)^t = 4
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t = 23.79 years
It will take 23.79 years for the amount to quadruple.