Question

Use the ordinary annuity formula to show the right way to determine the accumulated amount in the annuity if $30 is invested semiannually for 30 years at 5.5% compounded semiannually.

Answer 1

To determine the accumulated amount in the annuity, use the ordinary annuity formula A = P(1 + r/n)^(nt). For this example, the accumulated amount is $307.07 after 30 years.

Step-by-step explanation:

To determine the accumulated amount in the annuity, we can use the following formula:

A = P(1 + r/n)^(nt)

Where:

• A = Accumulated amount
• P = Principal amount (initial investment)
• r = Annual interest rate (as a decimal)
• n = Number of times the interest is compounded per year
• t = Number of years

For this specific example, we have:

• P = $30
• r = 5.5% = 0.055 (as a decimal)
• n = 2 (compounded semiannually)
• t = 30 years

Plugging these values into the formula, we can calculate:

A = 30(1 + 0.055/2)^(2*30) = $307.07 (rounded to the nearest cent)

Therefore, the accumulated amount in the annuity after 30 years is approximately $307.07.