Final answer:
To find the compound amount, we can use the formula A = P(1 + r/n)^(nt), where A is the compound amount, P is the principal amount, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years. In this case, the compound amount is approximately $832.08. To find the amount of interest earned, we subtract the principal amount from the compound amount, which is approximately $402.08.
Step-by-step explanation:
To find the compound amount and the amount of interest earned, we can use the formula:
A = P(1 + r/n)^(nt)
Where:
- A is the compound amount
- P is the principal amount (the initial deposit)
- r is the annual interest rate (written as a decimal)
- n is the number of times interest is compounded per year
- t is the number of years
In this case, P = $430, r = 6.8%, n = 2 (semiannual compounding), and t = 11 years. Plugging in the values, we get:
A = $430(1 + 0.068/2)^(2*11)
Calculating the compound amount, we find:
A = $430(1.034)^22 = $430 * 1.9365 ≈ $832.08
To find the amount of interest earned, we subtract the principal amount from the compound amount:
Interest earned = $832.08 - $430 = $402.08