$4500 is invested in an account at interest rate r,compounded continuously.Find the time required for the amount to triple.(Approximate the result to two decimal places. ) $r = 0.0315$
A)21.00 yr
B)20.00 yr
C)34.88 yr
D)24.00 yr
E)23.00 yr

Question

$4500 is invested in an account at interest rate r,compounded continuously.Find the time required for the amount to triple.(Approximate the result to two decimal places. )​ $r = 0.0315$ ​
A)21.00 yr
B)20.00 yr
C)34.88 yr
D)24.00 yr
E)23.00 yr

Quizplus · Accepted Answer

The formula for continuous compounding is $A = Pe^{rt}$, where $A$ is the amount of money accumulated after n years, including interest, $P$ is the principal amount (the initial amount of money), $r$ is the annual interest rate (decimal), and $t$ is the time the money is invested for in years. To triple the amount, we set $A = 3P$, so $3P = Pe^{rt}$. Simplifying, we get $3 = e^{rt}$. Substituting $r = 0.0315$, we solve for $t$: $3 = e^{0.0315t}$. Taking the natural logarithm of both sides, $ln(3) = 0.0315t$. Solving for $t$, $t = \frac{ln(3)}{0.0315} \approx 34.88$ years.

$4500 Is Invested in an Account at Interest Rate R,compounded r=0.0315r = 0.0315r=0.0315

$4500 Is Invested in an Account at Interest Rate R,compounded $r = 0.0315$