Liam puts $2,000 in the bank with a 3% annual interest rate compounded annually. If Liam does not touch his money, how much money will he have after two years?
Responses
A $2,000.06$2,000.06
B $2,060.00$2,060.00
C $2,120.00$2,120.00
D $2,121.80$2,121.80
To find the amount of money Liam will have after two years, we can use the formula for compound interest:
\[A = P \left(1 + \frac{r}{100}\right)^n\]
where:
A = the amount of money after the specified time period,
P = the initial amount of principal,
r = the annual interest rate, and
n = the number of compounding periods.
In this case, Liam initially puts $2,000 in the bank, the annual interest rate is 3%, and the interest is compounded annually. Therefore, we have:
\[A = 2,000 \left(1 + \frac{3}{100}\right)^2\]
Simplifying the equation, we get:
\[A = 2,000 \left(1 + \frac{3}{100}\right)^2\]
\[A = 2,000 \left(\frac{103}{100}\right)^2\]
\[A = 2,000 \cdot \frac{10,609}{10,000}\]
\[A = 2,120.90\]
After two years, Liam will have approximately $2,120.90 in the bank.
Therefore, the correct answer is C: $2,120.00.