Yes, that's correct! The simple interest formula helps you calculate the interest earned on an investment or loan over a specified period of time, but to find the total account value (or the total amount you will have at the end), you must add the interest earned to the principal amount.
The formula for calculating simple interest is:
\[ \text{Interest} = P \times r \times t \]
Where:
- \( P \) is the principal amount (the initial amount of money),
- \( r \) is the annual interest rate (in decimal form),
- \( t \) is the time (in years).
After calculating the interest, you can find the total amount by adding the interest to the principal:
\[ \text{Total Amount} = P + \text{Interest} \]
Putting it all together, you can also express it as:
\[ \text{Total Amount} = P + (P \times r \times t) \]
This can be simplified to:
\[ \text{Total Amount} = P(1 + rt) \]
This equation gives you the total amount in the account at the end of the time period, including both the principal and the interest earned.