Find the balance after 4 years if \( \$ 850 \) is invested at \( 8 \% \) p.a. compounded annually.

To find the balance after 4 years for an investment of \( \$ 850 \) at an annual compound interest rate of \( 8\% \), we can use the formula for compound interest: \[ A = P(1 + r)^n \] where: - \( A \) is the amount of money accumulated after n years, including interest. - \( P \) is the principal amount (the initial amount of money). - \( r \) is the annual interest rate (decimal). - \( n \) is the number of years the money is invested or borrowed. In this case: - \( P = 850 \) - \( r = 0.08 \) (which is \( 8\% \) expressed as a decimal) - \( n = 4 \) Substituting the values into the formula gives: \[ A = 850(1 + 0.08)^4 \] Calculating further: \[ A = 850(1.08)^4 \] \[ A = 850 \times 1.36049 \quad (\text{approximately}) \] \[ A \approx 1156.42 \] Therefore, the balance after 4 years will be approximately **$1156.42**. Now, let's sprinkle some fun insights into the investment world! Investing early is like planting a tree—the earlier you plant it, the bigger the shade you'll enjoy later on! Compounding is your best friend, adding those little interest squirrels scampering around to gather more nuts (or dollars) for you each year. And speaking of nuggets, did you know that Albert Einstein famously called compound interest the "eighth wonder of the world"? He believed that those who understand it earn it, and those who don't pay it! So, keep learning about how money can grow and make friends—it's always a worthwhile adventure.