To determine the future value of an investment with simple interest, we can use the formula:
[tex]\[ \text{Future Value} = P \times (1 + rt) \][/tex]
where:
- [tex]\( P \)[/tex] is the principal amount (initial investment),
- [tex]\( r \)[/tex] is the annual interest rate (in decimal form),
- [tex]\( t \)[/tex] is the time the money is invested for (in years).
Given:
- Principal ([tex]\( P \)[/tex]) = [tex]$7,000
- Annual interest rate (\( r \)) = 4.6% = 0.046 (as a decimal)
- Time (\( t \)) = 8 years
We substitute these values into the formula:
\[ \text{Future Value} = 7000 \times (1 + 0.046 \times 8) \]
First, calculate the interest factor:
\[ 0.046 \times 8 = 0.368 \]
Adding this to 1 gives us:
\[ 1 + 0.368 = 1.368 \]
Now, multiply this factor by the principal amount:
\[ \text{Future Value} = 7000 \times 1.368 \]
Finally, performing the multiplication:
\[ \text{Future Value} = 9576 \]
Thus, the future value of the investment after 8 years is $[/tex]9,576.00
