1. **State the problem:** Mr. Pattison invests $35000 at an annual interest rate of 7.65% compounded annually. We need to find how much money he will have after 5 years and check if it is enough for a 10% down payment on a $500000 house. 2. **Formula used:** The formula for compound interest is: $$ A = P \left(1 + \frac{r}{n}\right)^{nt} $$ where: - $A$ is the amount of money accumulated after $t$ years, including interest. - $P$ is the principal amount (initial investment). - $r$ is the annual interest rate (decimal). - $n$ is the number of times interest is compounded per year. - $t$ is the number of years. Since interest is compounded annually, $n=1$. 3. **Calculate the accumulated amount:** Given: - $P = 35000$ - $r = 7.65\% = 0.0765$ - $n = 1$ - $t = 5$ Substitute into the formula: $$ A = 35000 \left(1 + 0.0765\right)^5 = 35000 \times (1.0765)^5 $$ Calculate $(1.0765)^5$: $$ (1.0765)^5 \approx 1.4410 $$ So: $$ A \approx 35000 \times 1.4410 = 50435 $$ 4. **Calculate the required down payment:** The down payment is 10% of $500000$: $$ 0.10 \times 500000 = 50000 $$ 5. **Compare accumulated amount with down payment:** - Accumulated amount after 5 years: $50435$ - Required down payment: $50000$ Since $50435 > 50000$, the investment is sufficient to cover the down payment. **Final answers:** - Amount accumulated after 5 years: $50435$ - The initial investment is sufficient to cover the down payment.