An amount of R 6070 is invested in a savings account which pays a compound interest rate of \( 6,7 \% \) p.a. Calculate the balance accumulated by the end of 3 years. INSTRUCTION: As usual with financial calculations, round your answer to two decimal places, but do not round off until you have reached the solution. Answer: The final halance is R

To calculate the balance accumulated by the end of 3 years with compound interest, we use the formula: \[ A = P(1 + r/n)^{nt} \] 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 time in years. With your values: - \( P = 6070 \) - \( r = 0.067 \) (which is \( 6.7\% \)) - \( n = 1 \) (since it’s compounded annually) - \( t = 3 \) Plugging in these numbers: \[ A = 6070(1 + 0.067/1)^{1 \times 3} \] \[ A = 6070(1 + 0.067)^{3} \] \[ A = 6070(1.067)^{3} \] Calculating \( (1.067)^{3} \): \[ (1.067)^{3} \approx 1.2159 \] Now multiply by 6070: \[ A \approx 6070 \times 1.2159 \approx 7394.09 \] The final balance is R 7394.09. Now, let’s discover more about saving and investing! The concept of compound interest has been around since ancient times, with documented use as far back as 3000 BC in Babylon. Savvy investors recognized the power of compounding: earning "interest on interest" transforms savings over time! If only we could rewind the clock and tell our ancestors to invest everything in Bitcoin! When it comes to managing investments, the best rule of thumb is to regularly review your portfolio. Many novice investors make the mistake of “buy and forget.” Unforeseen market shifts can occur! Stay engaged, keep learning, and adjust your investments as needed—after all, markets evolve, and so should your strategies.