Question

The compound interest formula gives the total account value at the end of the time period.

If we want to find the interest accrued during that time, we need to subtract the principal from that total.

Answer 1

You're correct! The compound interest formula is often expressed as:

\[ A = P(1 + r/n)^{nt} \]

Where:
- \( A \) is the total 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 that interest is compounded per year.
- \( t \) is the number of years the money is invested or borrowed.

To find the interest accrued during the time period, you can calculate the total amount \( A \) using the formula and then subtract the principal \( P \) from it:

\[ \text{Interest Accrued} = A - P \]

Substituting the expression for \( A \):

\[ \text{Interest Accrued} = P(1 + r/n)^{nt} - P \]

This can be simplified to:

\[ \text{Interest Accrued} = P \left((1 + \frac{r}{n})^{nt} - 1\right) \]

This final expression gives you the total interest accrued over the specified time period.