What is the future, rounded to whole dollars, of $25,000 after 7 1/2 years, if money earns at an annual rate of 5.75% compounded continuosly?
To find the future value of an investment with continuously compounded interest, we can use the formula:
A = P * e^(rt)
Where:
A = the future value
P = the principal amount (initial investment)
e = the mathematical constant approximately equal to 2.71828
r = the annual interest rate (as a decimal)
t = the time in years
In this case:
P = $25,000
r = 5.75% = 0.0575 (as a decimal)
t = 7.5 years
Now, let's plug these values into the formula:
A = $25,000 * e^(0.0575 * 7.5)
To find the value of e^(0.0575 * 7.5), we can use a scientific calculator or an online calculator with the exponential function.
After calculating the value of e^(0.0575 * 7.5), we can multiply it by $25,000 to get the future value (A).
Finally, round the answer to the nearest whole dollar.