Final answer:
Using the compound interest formula, an investment of $480 with a 12% annual interest rate compounded monthly will be worth approximately $768.49 after 4 years.
Step-by-step explanation:
To calculate the worth of $480 in an account with a 12 percent annual interest rate compounded monthly after 4 years, we will use the formula for compound interest:
A = P (1 + \frac{r}{n}) ^{nt}
Where:
- A is the amount of money accumulated after n years, including interest.
- P is the principal amount ($480).
- r is the annual interest rate (decimal).
- n is the number of times that interest is compounded per year.
- t is the time the money is invested for in years.
In this case:
- P = $480
- r = 12% or 0.12
- n = 12 (since it's compounded monthly)
- t = 4 years
Now we can plug these values into the formula:
A = 480(1 + \frac {0.12}{12}) ^ {12 \times 4}
A = 480(1 + 0.01) ^ {48}
A = 480(1.01) ^ {48}
Calculating this value will give us the worth of the investment after 4 years. By using a calculator, we find that:
A ≈ 480(1.601032) ≈ $768.49
Therefore, the account will be worth approximately $768.49 after 4 years.