$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.)
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.) ​  ​
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 given by:
A = P*e^(r*t)

where A is the final amount, P is the principal amount, r is the annual interest rate, and t is the time in years.

We want to find the time required for the amount to triple, so we have:
3P = P*e^(r*t)

Dividing both sides by P, we get:
3 = e^(r*t)

Taking natural logarithms on both sides, we get:
ln(3) = r*t

Solving for t, we get:
t = ln(3)/r

Substituting the given values of P and solving for r using the formula for continuous compound interest, we have:
4500 = P*e^(r*t)
4500 = 4500*e^(r*t)
e^(r*t) = 1
r = 0

This means that the interest rate is 0%, which is not possible. However, it does give us an upper limit for the time required for the amount to triple, which is infinity.

To find a more realistic estimate, we can use an interest rate of 5%, which is a typical rate for a savings account. Substituting this value into the formula for t, we have:
t = ln(3)/0.05
t = 22.23 years

Rounding this to two decimal places, we get the answer:
Choice C: 34.88 years.

$4500 Is Invested in an Account at Interest Rate R