Continuously compounded interest be worth after 8 years is equals to $745.88.
" Continuously compounded interest is defined as the process of calculating interest for the given principal , rate of interest with time over an infinite number of periods."
Formula used
Continuously compounded interest
[tex]A = P e^{rt}[/tex]
A = final amount
P = initial Principal
r = rate of interest
t = time for which interest is applied
e = constant
value of e = 2.7183
According to the question,
Given,
Principal = $500
rate of interest 'r' = 5%
time 't' = 8years
Substitute the value in the formula to get Continuously Compounded interest ,
[tex]A = 500 (e^{(0.05)(8)} )[/tex]
[tex]= 500( e^{0.4} )[/tex]
Substitute the value of 'e' we get,
[tex]A= 500(2.7183^{0.4} )[/tex]
[tex]= 500(1.49176)\\= \$745.88[/tex]
Hence, continuously compounded interest be worth after 8 years is equals to $745.88.
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