The compound interest formula is given as [tex]\( A = P \left(1 + \frac{r}{n}\right)^{nt} \)[/tex].
Let's match each term to the part of the formula it represents:
1. Initial deposit:
- This represents the amount of money initially invested or deposited.
- In the compound interest formula, the initial deposit is denoted by [tex]\( P \)[/tex].
2. The number of years:
- This is the time period for which the money is invested or deposited.
- In the compound interest formula, the number of years is represented by [tex]\( t \)[/tex].
3. Total balance interest is computed in the account:
- This represents the amount of money in the account after interest has been applied over the given period.
- In the compound interest formula, the total balance is denoted by [tex]\( A \)[/tex].
4. The number of times in a year interest is compounded:
- This represents the frequency with which the interest is applied to the balance per year.
- In the compound interest formula, this frequency is denoted by [tex]\( n \)[/tex].
Finally, let's organize these matches in the table format:
[tex]\[
\begin{tabular}{|l|l|}
\hline
& A = P \left(1+\frac{r}{n}\right)^{nt} \\
\hline
A & total balance interest is computed in the account \\
\hline
P & initial deposit \\
\hline
r & annual interest rate \\
\hline
n & the number of times in a year interest is compounded \\
\hline
t & the number of years \\
\hline
\end{tabular}
\][/tex]
So, the matched terms are:
- [tex]\( A \)[/tex] corresponds to the total balance interest is computed in the account.
- [tex]\( P \)[/tex] corresponds to the initial deposit.
- [tex]\( r \)[/tex] corresponds to the annual interest rate.
- [tex]\( n \)[/tex] corresponds to the number of times in a year interest is compounded.
- [tex]\( t \)[/tex] corresponds to the number of years.
