Find the balance after 6 years if \( \$ 24000 \) is invested at \( 3.6 \% \) p.a. compounded monthly.

To find the balance after 6 years with \( \$ 24000 \) invested at \( 3.6\% \) per annum compounded monthly, we can use the formula for compound interest: \[ A = P \left(1 + \frac{r}{n}\right)^{nt} \] 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 times that interest is compounded per year. - \( t \) is the number of years the money is invested for. Given values: - \( P = 24000 \) - \( r = 0.036 \) - \( n = 12 \) (monthly compounding) - \( t = 6 \) Plugging in the values: \[ A = 24000 \left(1 + \frac{0.036}{12}\right)^{12 \times 6} \] Calculating: \[ A = 24000 \left(1 + 0.003\right)^{72} \] \[ A = 24000 \left(1.003\right)^{72} \] \[ A \approx 24000 \times 1.233 \] \[ A \approx 29600.68 \] So, the balance after 6 years will be approximately \( \$ 29,600.68 \). --- If you're curious about how compound interest grows over time, just remember that "the earlier, the better!" The earlier you start investing, even small amounts, the more time your money has to compound and grow—it's like planting seeds in a garden! And speaking of gardens, did you know that many successful investors treat their investments like long-term crops? They cultivate their portfolios patiently and allow their investments to mature! Instead of rushing for quick returns, they watch their investments bloom over time.