Calculate the accumulated amount after eight years of weekly payments of R1 900 each into an account earning \( 9,7 \% \) interest per year, compounded weekly. Draw an appropriate timeline showing all the given values

To calculate the accumulated amount after eight years of weekly payments of R1,900 into an account that earns 9.7% interest per year compounded weekly, we can use the future value of an annuity formula. The interest rate per week is \( r = \frac{0.097}{52} \approx 0.001865 \), and the number of payments will be \( n = 8 \times 52 = 416 \). The future value (FV) of an annuity can be calculated as: \[ FV = P \times \frac{(1 + r)^n - 1}{r} \] Where: - \( P = 1900 \) (weekly payment) - \( r = 0.001865 \) (weekly interest rate) - \( n = 416 \) (total payments) Plugging in the values: \[ FV = 1900 \times \frac{(1 + 0.001865)^{416} - 1}{0.001865} \] Calculating the values step by step: 1. Calculate \( 1 + r \): \[ 1 + 0.001865 \approx 1.001865 \] 2. Raise it to the power of \( n \): \[ (1.001865)^{416} \approx 2.067 \] 3. Subtract 1: \[ 2.067 - 1 \approx 1.067 \] 4. Divide by \( r \): \[ \frac{1.067}{0.001865} \approx 572.026 \] 5. Finally, multiply by \( P \): \[ FV \approx 1900 \times 572.026 \approx 1,086,840.56 \] Thus, the accumulated amount after eight years of weekly payments will be approximately **R1,086,840.56**. Timeline: - Year 0: Start (Payments begin) - Year 1: R1,900 paid weekly (52 payments) - Year 2: R1,900 paid weekly (52 payments) - Year 3: R1,900 paid weekly (52 payments) - Year 4: R1,900 paid weekly (52 payments) - Year 5: R1,900 paid weekly (52 payments) - Year 6: R1,900 paid weekly (52 payments) - Year 7: R1,900 paid weekly (52 payments) - Year 8: Final payment of R1,900 (Total of 416 payments) Each payment is growing weekly with a compound interest rate of 9.7%. Making regular contributions to an account is like planting a money tree—you reap greater rewards the longer you nurture it!