Comparing Tebogo's Parents' Loan Repayment Options

Let's evaluate both options using the given interest rates and time period to determine which option is better for Tebogo's parents. ### Option 1: Simple Interest For simple interest, the formula is: \[ A = P(1 + rt) \] Where: - \( A \) is the amount after time \( t \), - \( P \) is the principal amount (\( R 5 425 \)), - \( r \) is the annual interest rate (expressed as a decimal), and - \( t \) is the time in years. Given: - \( P = R 5 425 \), - \( r = 9.7\% = 0.097 \), - \( t = 2 \) years. Calculate the amount (\( A \)): \[ A = 5425 \times (1 + 0.097 \times 2) \] \[ A = 5425 \times (1 + 0.194) \] \[ A = 5425 \times 1.194 \] \[ A = 6481.45 \] So the total amount to be paid after 2 years with Option 1 is \( R 6 481.45 \). ### Option 2: Compound Interest For compound interest, the formula is: \[ A = P \left(1 + \frac{r}{n}\right)^{nt} \] Where: - \( A \) is the amount after time \( t \), - \( P \) is the principal amount (\( R 5 425 \)), - \( r \) is the annual interest rate (expressed as a decimal), - \( n \) is the number of times the interest is compounded per year, and - \( t \) is the time in years. Given: - \( P = R 5 425 \), - \( r = 9.5\% = 0.095 \), - \( n = 1 \) (compounded yearly), - \( t = 2 \) years. Calculate the amount (\( A \)): \[ A = 5425 \left(1 + \frac{0.095}{1}\right)^{1 \times 2} \] \[ A = 5425 \left(1 + 0.095\right)^2 \] \[ A = 5425 \times (1.095)^2 \] \[ A = 5425 \times 1.199025 \] \[ A = 6502.21 \] (rounded to the nearest cent) So the total amount to be paid after 2 years with Option 2 is \( R 6 502.21 \). ### Comparison: - Option 1 (Simple Interest): \( R 6 481.45 \) - Option 2 (Compound Interest): \( R 6 502.21 \) Since \( R 6 481.45 \) (Option 1) is less than \( R 6 502.21 \) (Option 2), Tebogo's father is correct in saying that Option 1 is the better option.