The formula for continuously compounded investments is expressed as follows:
[tex]A = Pe^{rt}[/tex]
P is the initial amount invested, r is the rate, and t is the amount of years the investment is compounded.
Convert the percentage into a decimal by dividing by 100:
[tex]4.55 \div 100 = 0.0455[/tex]
We now have all of our values, so plug them into the equation:
[tex]P = 15,000, r = 0.0455, t = 14[/tex]
[tex]15,000e^{(0.0455)(14)} = 15,000e^{0.637} = 28,361.999[/tex]
To round to the nearest cent, look at the thousandths value:
28,361.999
9 > 5
28,361.999 ≈ 28,362
The value of this investment will be $28,362.
