Question 612930
{{{A=Pe^(rt)}}} Start with the continuous compounding formula.



{{{10400=6500*e^(r*3)}}} Plug in {{{A=10400}}}, {{{P=6500}}}, and {{{t=3}}}.



{{{10400/6500=e^(r*3)}}} Divide both sides by {{{6500}}}.



{{{1.6=e^(r*3)}}} Evaluate {{{10400/6500}}} to get {{{1.6}}}.



{{{ln(1.6)=ln(e^(r*3))}}} Take the natural log of both sides.



{{{ln(1.6)=r*3*ln(e)}}} Pull down the exponent using the identity {{{ln(x^y)=y*ln(x))}}}.



{{{ln(1.6)=r*3*1}}} Evaluate the natural log of 'e' to get 1.



{{{ln(1.6)=r*3}}} Multiply and simplify.



{{{0.470003629245736=r*3}}} Evaluate the natural log of {{{1.6}}} to get {{{0.470003629245736}}} (this value is approximate).



{{{0.470003629245736/3=r}}} Divide both sides by {{{3}}} to isolate 'r'.



{{{0.156667876415245=r}}} Evaluate {{{0.470003629245736/3}}} to get {{{0.156667876415245}}}.



{{{r=0.156667876415245}}} Flip the equation.



{{{r=0.1567}}} Round to the nearest ten-thousandth.



So the interest rate is roughly <font color="red">15.67%</font>