$8000 invested in an account that pays 4% compounded daily will be worth $10584.8 after 7 years
The continuous compounding formula should be used when a statement that the amount is "compounded continuously" is made in a clear statement. This formula employs the mathematical constant "e," which has a value of about 2.7182818. The formula for continuous compounding is displayed below.
Compound interest is of different forms of compounding frequency. We are dealing with interest that is continuously compounded in this problem.
So, we need to use the formula FV=Pe^{rt}
where:
FV is the future value.
r is the rate of interest.
t is the time in years.
e is Euler's number
Given:
P=8,000
r=0.07
t=7
Using the formula for the future value of compound interest FV=Pe^{rt} , we have,
[tex]FV = 8000e^{0.04*7} \\FV = 8000e^{0.28} \\FV = 8000*1.3231\\= $10584.8[/tex]
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