3.5. Diego took out a loan at \( 6.2 \% \) p.a. compound interest. Calculate the amount he borrowed if he repays the loan in four years with R 720000.

To find out how much Diego borrowed, we can use the formula for compound interest, which is expressed as: \[ A = P(1 + r)^n \] Where: - \( A \) is the total amount after interest (R 720,000), - \( P \) is the principal amount (the initial loan amount), - \( r \) is the annual interest rate (6.2% or 0.062), - \( n \) is the number of years (4). We need to rearrange the formula to solve for \( P \): \[ P = \frac{A}{(1 + r)^n} \] Plugging in the values: \[ P = \frac{720000}{(1 + 0.062)^4} \] \[ P = \frac{720000}{(1.062)^4} \] \[ P = \frac{720000}{1.2625} \] \[ P ≈ 570,557.99 \] So, Diego borrowed approximately R 570,558. But wait! Just like in history where one discovers ancient maps leading to treasure, exploring loan repayments can uncover real financial strategies. Diego's choice of a loan at a relatively low rate proves that understanding interest rates can lead you down a path of financial wisdom! If you're pondering how to tackle loans or investments, you might want to budget wisely. A common mistake is underestimating future expenses or not considering how interest compounds. Always factor in unexpected costs and remember, a little planning goes a long way in ensuring your financial future is as bright as the sun on a summer’s day!