Final answer:
To calculate the future value of a $600 investment with a 4.5% annual growth rate compounded monthly after 1 year, use the compound interest formula. The amount turns out to be approximately $627.11.
Step-by-step explanation:
To determine how much $600 invested at a growth rate of 4.5% annually compounded monthly will be at the end of 1 year, we use the compound interest formula:
A = P(1 + r/n)(nt)
Where:
A = the future value of the investment/loan, including interest
P = the principal investment amount ($600)
r = the annual interest rate (decimal)
n = the number of times that interest is compounded per year
t = the time the money is invested for, in years
Given the values:
- P = $600
- r = 4.5/100 = 0.045
- n = 12 (since the interest is compounded monthly)
- t = 1 year
Now, we can calculate the amount after 1 year:
A = 600(1 + 0.045/12)(12*1)
A = 600(1 + 0.00375)12 = 600(1.00375)12
A = 600 * 1.04685
A ≈ $627.11
So, after 1 year, the investment will be approximately $627.11.