Question 556128
1. What annual rate compounded continuously is equivalent to an effective rate of 5%?
Continuous interest formula: {{{A = P*e^(rt)}}} for 1 yr: {{{A = P*e^r}}}
Simple interest formula for 1 yr: A = P*(1+r)
A simple equation
{{{e^r}}} = 1.05
Find the nat log of both sides (nat log of e = 1)
r = ln(1.05)
r = .04879 ~ 4.88% cont interest is equiv to 5% simple int for 1 yr
:
2. What annual rate r compounded continuously is equivalent to a nominal rate if 6% compounded semi-annually?
Compounded semi annually: (1.03)^2 = 1.0609 
{{{e^r}}} = 1.0609
r = ln(1.0609)
r = .0591 ~ 5.91% cont interest
:
3. If interest is compounded continuously at an annual rate of 0.07, how many years would it take for a principal P to triple? 
:
{{{e^(.07t)}}} = 3
.07t = ln(3)
.07t = 1.0986
t = {{{1.0986/.07}}}
t = 15.7 ~ 16 yrs to triple