Question
What is the formula to calculate the future balance of an investment account that earns 6% annual interest compounded monthly?
Answers
Answered by
GPT-4o mini
The formula to calculate the future balance of an investment account with compound interest is given by:
\[
A = P \left(1 + \frac{r}{n}\right)^{nt}
\]
Where:
- \(A\) = the future value of the investment/loan, including interest
- \(P\) = the principal investment amount (the initial deposit or loan amount)
- \(r\) = the annual interest rate (decimal)
- \(n\) = the number of times that interest is compounded per year
- \(t\) = the number of years the money is invested or borrowed
For your specific case:
- The annual interest rate \(r\) is 6%, which is \(0.06\) in decimal form.
- Since the interest is compounded monthly, \(n = 12\).
Thus, the formula for your investment earning 6% annual interest compounded monthly would be:
\[
A = P \left(1 + \frac{0.06}{12}\right)^{12t}
\]
This formula can be used to find out how much your investment will grow over time, given the initial investment amount \(P\) and the number of years \(t\).
\[
A = P \left(1 + \frac{r}{n}\right)^{nt}
\]
Where:
- \(A\) = the future value of the investment/loan, including interest
- \(P\) = the principal investment amount (the initial deposit or loan amount)
- \(r\) = the annual interest rate (decimal)
- \(n\) = the number of times that interest is compounded per year
- \(t\) = the number of years the money is invested or borrowed
For your specific case:
- The annual interest rate \(r\) is 6%, which is \(0.06\) in decimal form.
- Since the interest is compounded monthly, \(n = 12\).
Thus, the formula for your investment earning 6% annual interest compounded monthly would be:
\[
A = P \left(1 + \frac{0.06}{12}\right)^{12t}
\]
This formula can be used to find out how much your investment will grow over time, given the initial investment amount \(P\) and the number of years \(t\).