Sure! Let's calculate the future value of an investment given a principal amount, an annual interest rate, and a number of years, compounded annually.
Here's the problem we're solving:
- Principal (P): [tex]$4600
- Annual interest rate (r): 7% or 0.07
- Number of years (t): 5 years
We'll use the compound interest formula:
\[ A = P (1 + r)^t \]
Where:
- \( A \) is the amount of money accumulated after n years, including interest.
- \( P \) is the principal amount (the initial amount of money).
- \( r \) is the annual interest rate (decimal).
- \( t \) is the time the money is invested for in years.
Let's plug in the values into the formula:
\[ A = 4600 \times (1 + 0.07)^5 \]
\[ A = 4600 \times (1.07)^5 \]
Now, compute \( (1.07)^5 \):
\[ (1.07)^5 \approx 1.402552 \]
Then multiply this value by the principal:
\[ A \approx 4600 \times 1.402552 \]
\[ A \approx 6451.73796 \]
Rounding to the nearest dollar:
\[ A \approx 6452 \]
So, the investment will be worth approximately $[/tex]6452 after 5 years.
