1. The problem involves finding the nearest dollar amount for a compound interest calculation. 2. The formula for compound interest is $$A = P \left(1 + \frac{r}{n}\right)^{nt}$$ where: - $A$ is the amount of money accumulated after $t$ years, including interest. - $P$ is the principal amount (initial investment). - $r$ is the annual interest rate (decimal). - $n$ is the number of times interest is compounded per year. - $t$ is the time the money is invested for in years. 3. To find the nearest dollar, calculate $A$ using the formula and then round the result to the nearest whole number. 4. Example: If $P=1000$, $r=0.05$, $n=4$, and $t=3$, then $$A = 1000 \left(1 + \frac{0.05}{4}\right)^{4 \times 3} = 1000 \left(1 + 0.0125\right)^{12} = 1000 \times 1.16075 = 1160.75$$ 5. Rounding $1160.75$ to the nearest dollar gives $1161$. 6. Therefore, the amount after 3 years is approximately $1161$ dollars.