To solve the problem of finding how much money was in the Maendaco youth group's account after one year, we need to use the compound interest formula. The formula for compound interest is:
[tex]\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \][/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 (decimal).
- [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:
- [tex]\(P = 20{,}000\)[/tex]
- [tex]\(r = 9\% = 0.09\)[/tex]
- [tex]\(n = 1\)[/tex] (assuming the interest is compounded annually)
- [tex]\(t = 1\)[/tex] year
Let's plug these values into the formula:
[tex]\[ A = 20{,}000 \left(1 + \frac{0.09}{1}\right)^{1 \cdot 1} \][/tex]
First, calculate the rate divided by n:
[tex]\[ \frac{0.09}{1} = 0.09 \][/tex]
Next, add 1 to the rate:
[tex]\[ 1 + 0.09 = 1.09 \][/tex]
Then, raise this to the power of [tex]\(nt\)[/tex]:
[tex]\[ 1.09^{1 \cdot 1} = 1.09 \][/tex]
Finally, multiply this by the principal:
[tex]\[ A = 20{,}000 \times 1.09 = 21{,}800 \][/tex]
Therefore, the amount of money in the account after one year is:
[tex]\[ \boxed{21{,}800} \][/tex]
