To calculate the amount James Parris will have after five years, we can use the future value of an annuity formula, since James is saving a fixed amount annually:

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

Where:

• $FV$ is the future value (the amount James will have),
• $P = 4750$ is the annual payment,
• $r = 0.05$ is the annual interest rate (5%),
• $n = 5$ is the number of years.

Now, let's plug in the values and calculate:

$FV = 4750 \times \frac{(1 + 0.05)^5 - 1}{0.05}$

$FV = 4750 \times \frac{(1.27628 - 1)}{0.05}$

$FV = 4750 \times \frac{0.27628}{0.05}$

$FV = 4750 \times 5.5256$

$FV \approx 26,748.60$

Thus, after five years, James will have approximately $26,748.60 for his down payment.

Would you like more details or have any questions?

Here are 5 related questions to explore further:

1. How would the final amount change if the interest rate were 6% instead of 5%?
2. What if James saved $5,000 a year instead of $4,750?
3. How does the future value change if James saves for 10 years instead of 5?
4. What would be the amount if James made quarterly deposits instead of yearly ones?
5. What happens if the interest rate compounds monthly instead of annually?

Tip: The more frequent the compounding periods, the greater the future value will be due to interest on interest (compound interest effect).