Question

what is the future value of an annuity where $4,000 is deposited every 6 months for 9 years, and earns interest at 10 percent compounded semi-annually? show your calculations.

Answer 1

The future value of the annuity is approximately $112529.538.

Calculating the Future Value of the Annuity

Here's how to calculate the future value of the annuity, along with the calculations:

Formula:

The future value (FV) of an annuity can be calculated using the following formula:

FV =
`P * (((1 + r)^(n - 1)))/(r)`

where:

P is the payment amount ($4,000)

r is the interest rate per period (10% / 2 = 5% for semi-annual)

n is the total number of periods (9 years * 2 periods/year = 18 periods)

Calculation:

FV = $
`4,000 * (((1 + 0.05)^(18 - 1)))/(0.05)`

FV ≈ $
`4,000 * ((4.5563196 - 1))/(0.05)`

FV ≈ $112529.538

Therefore, the future value of the annuity is approximately $112529.538.