18.0k views
1 vote
Find the time it takes for $5,900 to double when invested at an annual interest rate of 4%, compounded continuously.

User Seemly
by
7.0k points

1 Answer

5 votes

Final answer:

It takes approximately 17.33 years for $5,900 to double at an annual interest rate of 4%, compounded continuously. We use the continuous compounding formula A = Pert, solve for t, and get t ≈ 17.33 when A is twice P.

Step-by-step explanation:

To find the time it takes for $5,900 to double when invested at an annual interest rate of 4%, compounded continuously, we can use the formula for continuous compounding:

A = Pert

where:


A is the final amount that the initial investment grows to after interest.





To double the money, A will be 2 times P ($5,900). So, our equation becomes:

2 * $5,900 = $5,900 * e0.04t

Solving for t, we divide both sides by $5,900, getting:

2 = e0.04t

Take the natural logarithm of both sides:

ln(2) = 0.04t

Divide by 0.04 to isolate t:

t = ln(2) / 0.04

Finally, calculate t:

t ≈ 17.33 years

So, it takes approximately 17.33 years for $5,900 to double at an annual interest rate of 4%, compounded continuously.

User Pedro Nasser
by
8.5k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories