Comparing Total Cost of Borrowing R5,425 for 2 Years under Simple and Compound Interest

To determine which loan option is better, we need to compare the total amount of money that will be owed under each option after 2 years. We'll start with calculating the total amount for each option. ### Option 1: Simple Interest The formula for simple interest is: \[ A = P(1 + rt) \] where: - \( A \) is the total amount owed - \( P \) is the principal amount (R5 425) - \( r \) is the annual interest rate (9.7% or 0.097) - \( t \) is the time in years (2 years) \[ A = 5,425(1 + 0.097 \times 2) \] \[ A = 5,425(1 + 0.194) \] \[ A = 5,425 \times 1.194 \] \[ A = 6,479.45 \] So, the total amount to be repaid under Option 1 is R6,479.45. ### Option 2: Compound Interest The formula for compound interest is: \[ A = P \left(1 + \frac{r}{n}\right)^{nt} \] where: - \( A \) is the total amount owed - \( P \) is the principal amount (R5 425) - \( r \) is the annual interest rate (9.5% or 0.095) - \( n \) is the number of times the interest is compounded per year (1 in this case since it's compounded yearly) - \( t \) is the time in years (2 years) Since the interest is compounded yearly, \( n = 1 \): \[ A = 5,425 \left(1 + \frac{0.095}{1}\right)^{1 \times 2} \] \[ A = 5,425 \left(1 + 0.095\right)^{2} \] \[ A = 5,425 \left(1.095\right)^{2} \] \[ A = 5,425 \left(1.199025\right) \] \[ A = 6,504.91 \] (approximately) So, the total amount to be repaid under Option 2 is R6,504.91. ### Comparing the Options - Option 1 total repayment: R6,479.45 - Option 2 total repayment: R6,504.91 ### Conclusion Since R6,479.45 < R6,504.91, Option 1 with simple interest is indeed the cheaper option. Tebogo’s father is correct in stating that Option 1 is the better option.