Answer:
The future value (\(FV\)) of a deposit with compound interest can be calculated using the compound interest formula:
\[ FV = P \times \left(1 + \frac{r}{n}\right)^{nt} \]
where:
- \(P\) is the principal amount (initial deposit),
- \(r\) is the annual interest rate (as a decimal),
- \(n\) is the number of times interest is compounded per year,
- \(t\) is the number of years.
In this case:
- \(P = $3000\),
- \(r = 6\% = 0.06\) (as a decimal),
- \(n = 12\) (monthly compounding),
- \(t = 15\) years.
Substitute these values into the formula and calculate the future value (\(FV\)).
The future value (\(FV\)) of a $3000 deposit with 6% interest compounded monthly over 15 years can be calculated using the compound interest formula:
\[ FV = 3000 \times \left(1 + \frac{0.06}{12}\right)^{12 \times 15} \]
Let's calculate this value.
Explanation:
The future value (\(FV\)) of a $3000 deposit with a 6% interest rate compounded monthly over 15 years is approximately $7121.05.