Question

(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.)

Answer 1

Answer:

Explanation:

Given

rate of interest= 8%

For continuously compounded interest

$A=Pe^{rt}$

Where A=amount

P=Principal

r=rate of interest

t=time

$2P=Pe^{0.08t}$

$2=e^{0.08t}$

taking log both sides

$\ln 2=0.08 t$

$t=\frac{\ln 2}{0.08}$

t=8.66 yr

(b)Equivalent annual interest

$2=(1+i)^t$

$2=(1+i)^{8.66}$

$2^{0.1154}=1+i$

$i+1=1.0832$

i=0.0832

8.32 %