To determine how much the [tex]$7,000 will be worth when you graduate from med school in seven years with an annual interest rate of 3%, we'll use the compound interest formula.
The compound interest formula is:
\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \]
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).
- \( n \) is the number of times interest is compounded per year.
- \( t \) is the number of years.
In this case:
- \( P = 7000 \)
- \( r = 0.03 \) (3% as a decimal)
- \( n = 1 \) (if the interest is compounded annually)
- \( t = 7 \) years
Substituting these values into the formula gives:
\[ A = 7000 \left(1 + \frac{0.03}{1}\right)^{1 \times 7} \]
\[ A = 7000 \left(1 + 0.03\right)^7 \]
\[ A = 7000 (1.03)^7 \]
Now calculate \((1.03)^7\):
\[ (1.03)^7 \approx 1.225043 \]
Multiply this by the principal amount:
\[ A = 7000 \times 1.225043 \]
\[ A \approx 8609.12 \]
Therefore, the amount will be worth approximately $[/tex]8609.12 when you graduate from med school in seven years, given an annual interest rate of 3%.
