Question 1139828
An initial deposit is made in a bank account. Find the interest rate, r , if the interest is compounded continuously and no withdrawals or further deposits are made. Round to the nearest hundredth of a percent.
Initial Amount: $3,500
Amount in 5 years: $5,100
<pre>Formula for interest rate (r), with future value (FV), present value (PV), and time (t), in years, KNOWN: {{{matrix(1,3, r, "=", ln (FV/PV)/t)}}}
{{{highlight_green(matrix(1,11, r, "=", ln ("5,100"/"3,500")/5, "=====>", r, "=", ".075296,", or, ".0753,", or, "7.53%"))}}}

<b><u>OR</b></u>

Using the future value formula for continuous compounding, or, {{{matrix(1,3, A, "=", Pe^(rt))}}}, we get: 
{{{matrix(1,3, "5,100", "=", "3,500"e^(5t))}}} ------- Substituting 5,100 for A, 3,500 for P, and 5 for r
{{{matrix(1,3, "5,100"/"3,500", "=", e^(5r))}}}
{{{matrix(1,3, 51/35, "=", e^(5r))}}}
{{{matrix(1,3, 5r, "=", ln (51/35))}}} -------- Converting to EXPONENTIAL form
{{{highlight_green(matrix(1,12, "r,", or, interest, rate, "=", ln (51/35)/5, "=", ".075296,", or, ".0753,", or, "7.53%"))}}}