# (a) How long will it take an investment to double in value if the interest rate is 3% compounded continuously? (Round your answer to two decimal places.)23.10yr(b) What is the equivalent annual interest rate? (Round your answer to two decimal places.)0.03x %Enhanced FeedbackPlease try again using one of the following formulas. If the interest is compounded periodically, the value of the investment in terms of time is A(t) A1 ,and if compoundedcontinuously, the the value of the investment is A(t)Aoet, where r is the nominal annual interest rate, t is the total time in years, and n is the number of compounding periods peryear.

Question
50 views help_outlineImage Transcriptionclose(a) How long will it take an investment to double in value if the interest rate is 3% compounded continuously? (Round your answer to two decimal places.) 23.10 yr (b) What is the equivalent annual interest rate? (Round your answer to two decimal places.) 0.03 x % Enhanced Feedback Please try again using one of the following formulas. If the interest is compounded periodically, the value of the investment in terms of time is A(t) A1 , and if compounded continuously, the the value of the investment is A(t) Aoet, where r is the nominal annual interest rate, t is the total time in years, and n is the number of compounding periods per year. fullscreen
check_circle

Step 1

Future value of invested amount A(0) at any time t, A(t) = A(0)ert where r is the interest rate compounded continuously and t is the time period.

Step 2

Part (a)

A(t) = 2 x A(0)

r = 3% = 0.03; we have to find t

Hence, 2 x A(0) = A(0)e0.03t

Hence, 2 = e0.03t

Take log to the natural base e on both sides,

0.03t = ln(2) = 0.6931

Hence, t = 0.6931 / 0.03 = 23.10 years

Step 3

Part (b)

If R is the effective annual rate, then

1 + R = er = e0.03 = 1.0305

Hence, R = 1.0305 - 1= 0.0305 = 3.05%

### Want to see the full answer?

See Solution

#### Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour.*

See Solution
*Response times may vary by subject and question.
Tagged in

### Calculus 