Final answer:
The value of the investment after 1 year is approximately $820.16.
Step-by-step explanation:
To calculate the value of the investment after 1 year, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount (the value of the investment after 1 year)
P = the principal amount (the initial investment)
r = the annual interest rate (as a decimal)
n = the number of times that interest is compounded per year
t = the number of years
In this case, P = $800, r = 2.4% = 0.024 (as a decimal), n = 4 (quarterly compounding), and t = 1 year. We can plug in these values into the formula:
A = 800(1 + 0.024/4)^(4*1)
Simplifying the equation, we get:
A = 800(1.006)^4
Using a calculator, we can find that A is approximately $820.16.