To find the future value of an ordinary annuity, we use the formula:

$FV = P \times \frac{(1 + r)^n - 1}{r}$

where:

• $P$ is the payment amount per period,
• $r$ is the interest rate per period,
• $n$ is the total number of payments.

Given Data:

• Payment amount per period ( $P$ ): $4,000
• Interest rate (annual): 8%
• Compounding frequency: Quarterly
• Time period: 2 years

Step-by-Step Solution:

1. Determine the interest rate per period ($r$):

   • Annual interest rate = 8%, so quarterly rate = $\frac{8\%}{4} = 2\% = 0.02$.

2. Determine the total number of payments ( $n$ ):

   • 2 years with quarterly payments: $2 \times 4 = 8$ payments.

3. Plug values into the formula:

   $FV = 4000 \times \frac{(1 + 0.02)^8 - 1}{0.02}$

4. Calculate each part:

   • $(1 + 0.02)^8 = 1.171659$
   • Subtract 1: $1.171659 - 1 = 0.171659$
   • Divide by $r$: $\frac{0.171659}{0.02} = 8.58295$
   • Multiply by $P$: $4000 \times 8.58295 = 34331.80$

Final Answer:

The future value of the annuity is approximately $34,331.80.

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Would you like further details or have any questions?

Here are some related questions for further exploration:

1. How would the future value change if the payments were made monthly instead of quarterly?
2. What if the interest rate were compounded monthly at the same annual rate?
3. How is the formula adjusted for an annuity due rather than an ordinary annuity?
4. What impact does increasing the payment amount have on the future value?
5. How does changing the interest rate affect the future value of the annuity?

Tip: For ordinary annuities, payments are made at the end of each period, so ensure the formula used aligns with the timing of payments.