For us to determine how much the account will be in 5 years at compounded continuously, we will be using the following formula:
[tex]\text{ A = P}_0e^{rt}[/tex]Where,
P = Principal amount (Initial Value)
A = Final amount (Future Value)
r = interest rate (in decimal)
t = time (in years)
e = mathematical constant approximately 2.7183
Given:
P = $5,000
r = 6% = 6/100 = 0.06
t = 5 years
We get,
[tex]\text{ A = P}_0e^{rt}[/tex][tex]\text{ A = (5,000)(2.7183)}^{(0.06)(5)}[/tex][tex]\text{ A = (5,000)(2.7183)}^{0.3}[/tex][tex]\text{ A = (5,000)(}1.34986151469)[/tex][tex]\text{ A = }6,749.30757343\text{ }\approx\text{ \$6,749.30}[/tex]Therefore, in 5 years, at 6% compounded continuously, your account will be $6,749.30
