To calculate the future value of an annuity where regular payments are made, the formula is:

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

Where:

• $FV$ is the future value of the annuity.
• $P$ is the annual payment (10,000 in this case).
• $r$ is the annual interest rate (8%, or 0.08).
• $n$ is the number of payments (10 years).

Given dataTo calculate the future value of an annuity where regular payments are made, the formula is:

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

Where:

• $FV$ is the future value of the annuity.
• $P$ is the annual payment (10,000 in this case).
• $r$ is the annual interest rate (8%, or 0.08).
• $n$ is the number of payments (10 years).

Given

• $P = 10,000$
• $r = 0.08$
• $n = 10$
• $(1 + r)^{10} = 2.15892500$

Plugging in the values:

$FV = 10,000 \times \frac{2.15892500 - 1}{0.08}$

$FV = 10,000 \times \frac{1.15892500}{0.08}$

$FV = 10,000 \times 14.4865625$

$FV = 144,865.625$

So, the future value of the annuity is $144,865.63 (rounded to two decimal places).

Would you like more details, or do you have any questions?

Here are five related questions to explore further:

1. How does changing the interest rate affect the future value of the annuity?
2. What would be the future value if Z invested $5,000 instead of $10,000 each year?
3. How would the calculation change if the interest were compounded semi-annually instead of annually?
4. What is the present value of the annuity using the same interest rate?
5. How does the number of years (n) impact the future value?

Tip: Always double-check the number of periods and the rate to ensure they align with the compounding frequency (e.g., annual, semi-annual).