To find the compound amount on a deposit after a certain time with a given interest rate, we can use the compound interest formula:
[tex]\[ A = P(1 + r/n)^{nt} \][/tex]
Where:
- [tex]\( A \)[/tex] is the amount of money accumulated after n years, including interest.
- [tex]\( P \)[/tex] is the principal amount (the initial amount of money).
- [tex]\( r \)[/tex] is the annual interest rate (in decimal form).
- [tex]\( n \)[/tex] is the number of times that interest is compounded per year.
- [tex]\( t \)[/tex] is the time the money is invested for, in years.
Given that the deposit is [tex]$700, the annual interest rate is 6% (or 0.06 in decimal form), and interest is compounded annually (so \( n = 1 \)) over 5 years, we can plug these values into the formula to calculate the compound amount.
First, convert the annual interest rate from a percentage to a decimal by dividing by 100:
\[ 6\% = \frac{6}{100} = 0.06 \]
Since the interest is compounded annually, that means \( n = 1 \). Now we can substitute the given values into the formula:
\[ A = P(1 + r/n)^{nt} \]
\[ A = 700(1 + 0.06/1)^{(1)(5)} \]
\[ A = 700(1 + 0.06)^5 \]
\[ A = 700(1.06)^5 \]
Now we just need to calculate the value of \( (1.06)^5 \) and then multiply by 700.
Using a calculator:
\[ (1.06)^5 \approx 1.3382255776 \]
So now we can find the compound amount:
\[ A \approx 700 \times 1.3382255776 \]
\[ A \approx 937.75790432 \]
Rounding to the nearest cent, if necessary:
\[ A \approx $[/tex]937.76 \]
Therefore, the compound amount on a deposit of [tex]$700 at 6% interest compounded annually for 5 years is approximately $[/tex]937.76.
