Find the compound amound for the deposit and the anount of intorest eamed
318.000 at $5 \%$ compounded monthily for 11 years
The compound amount after 11 years is $\$$
(Do not round until the final answer. Then round to the nearest cent as needed.)
The amount of interest earned is $\$ \square$.
(Do not round until the final answer. Then round to the nearest cent as needed.)
Answer
Rounding to the nearest cent, the compound amount after 11 years is \(\boxed{\$550545.01}\) and the amount of interest earned is \(\boxed{\$232545.01}\).
Step 1 ：Given that the principal amount (P) is $318,000, the annual interest rate (r) is 5% or 0.05 in decimal, the number of times that interest is compounded per year (n) is 12 (since it's compounded monthly), and the time the money is invested for in years (t) is 11.
Step 2 ：We use the compound interest formula A = P(1 + r/n)^(nt) to find the amount of money accumulated after n years, including interest.
Step 3 ：Substituting the given values into the formula, we get A = 318000(1 + 0.05/12)^(12*11) = 550545.0141559908.
Step 4 ：To find the amount of interest earned, we subtract the initial principal from the compound amount. So, the interest earned is 550545.0141559908 - 318000 = 232545.0141559908.
Step 5 ：Rounding to the nearest cent, the compound amount after 11 years is \(\boxed{\$550545.01}\) and the amount of interest earned is \(\boxed{\$232545.01}\).
