The amount of money in an account with continuously compounded interest is given by the formula A = Pert, where P is the principal, r is the annual interest rate, and t is the time in years. Calculate to the nearest tenth of a year how long it takes for an amount of money to double if interest is compounded continuously at 5.5%.

Question

anonymous · Answer

12.6 years

anonymous · Answer

A = Pe^rt
2P = Pe^.055t
2 = e^.055t
ln 2 = lne^.055t
ln 2 = .055t
(ln 2)/.055 = t