Answer:
Explanation:
To calculate the final account balance for a savings account with an initial deposit of $5,460.75, compounded semiannually with an interest rate of 3.92%, for 51 months, we need to use the formula:
A = P * (1 + r/n)^(nt)
where A is the final account balance, P is the initial deposit, r is the interest rate (as a decimal), n is the number of times the interest is compounded in a year, t is the number of years, and nt is the number of compounding periods.
In this case, n = 2 (since the interest is compounded semiannually), r = 3.92%/100 = 0.0392, t = 51 months / 12 months/year = 4.25 years, and nt = 2 * 4.25 = 8.5.
Substituting the values into the formula, we get:
A = $5,460.75 * (1 + 0.0392/2) ^ (8.5)
A = $5,460.75 * 1.0196^8.5
A = $5,460.75 * 1.2408
A = $6790.32
So, the final account balance if the initial deposit is invested with interest compounded semiannually is $6790.32.
B) Comparing the final account balance of the simple interest account and the compound interest account, we can see that the compound interest account yields a higher balance ($6790.32) than the simple interest account ($6370.51). This is because compounding interest allows for the interest earned in one period to be reinvested, so the interest earns interest in future periods, which increases the overall amount of interest earned over time. In contrast, simple interest is calculated only on the initial deposit, so the amount of interest earned remains constant over time.