Question

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 hundredth of a year how long it takes for an amount of money to double if interest is compounded continuously at 3.1%.
Round to the nearest tenth.

Answer 1

A=future amount
P=present amount
r=rate in decimal
t=time in years


when A=2P, then that is double
A=Pe^(rt)
2P=Pe^(rt)
divide by P
2=e^(rt)
r=3.1% or 0.031 solve for t
2=e^(0.031t)
take the ln of both sides
ln(2)=0.031t
divide both sides by 0.031
(ln(2))/0.031=t
use calculator
22.359=t
round to tenth
22.4 years to double

Answer 2

It will take approximately 1.04 years to double the principal amount.