(a) How long will it take an investment to double in value if the interest rate is 8% compounded continuously? (Round your answer to two decimal places.) yr (b) What is the equivalent annual interest rate? (Round your answer to two decimal places.)
Added by Adri-N A.
Step 1
08), and the investment doubles in value, we have: \[2P = P \times e^{0.08t}\] Solving for t: \[2 = e^{0.08t}\] \[ln(2) = 0.08t\] \[t = \frac{ln(2)}{0.08} \approx 8.66 \text{ years}\] Show more…
Show all steps
Your feedback will help us improve your experience
Sikandar Baig and 65 other Physics 101 Mechanics educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
(a) How long does it take for an investment to double in value if it is invested at $8 \%$ compounded monthly? (b) How long does it take if the interest is compounded continuously?
Exponential and Logarithmic Functions
Financial Models
How long would it take an investment to double under each of the following conditions? (a) Interest is 4.5% compounded monthly. (Round your answer to three decimal places.) yr (b) Interest is 8% compounded continuously. (Round your answer to three decimal places.) yr
Keondre P.
The time $t$ in years for an amount of money invested at an interest rate $r$ (in decimal form) to double is given by $$t(r)=\frac{\ln 2}{\ln (1+r)}$$ This is the doubling time. Find the doubling time to the nearest tenth for an investment at each interest rate. (a) $2 \%$ (or 0.02 ) (b) $5 \%$ (or 0.05 ) (c) $8 \%$ (or 0.08 )
Inverse, Exponential, and Logarithmic Functions
Common and Natural Logarithms
Recommended Textbooks
University Physics with Modern Physics
Physics: Principles with Applications
Fundamentals of Physics
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD