Question 3 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 earning 9.7% interest per year, compounded weekly, we first need to identify a formula that incorporates the periodic deposits and interest rate. The future value of a series of cash flows can be calculated using the future value of an ordinary annuity formula: \[ FV = P \times \frac{(1 + r)^n - 1}{r} \] Where: - \( FV \) = future value - \( P \) = payment per period (R1,900) - \( r \) = interest rate per period - \( n \) = total number of payments Given: - Annual interest rate = 9.7%, so weekly rate \( r = \frac{0.097}{52} \approx 0.0018673 \) (as there are 52 weeks in a year) - Total number of payments \( n = 8 \, \text{years} \times 52 \, \text{weeks/year} = 416 \) Now, plug in the values into the formula: \[ FV \approx 1900 \times \frac{(1 + 0.0018673)^{416} - 1}{0.0018673} \] After calculating, you'll find that the future value represents the total accumulated amount after the eight years. Now, let’s create a timeline. It will look something like this: | Years | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | |-----------|-----|-----|-----|-----|-----|-----|-----|-----| | Payments | R1,900 | R1,900 | R1,900 | R1,900 | R1,900 | R1,900 | R1,900 | R1,900 | | Interest | Compounded | Compounded | Compounded | Compounded | Compounded | Compounded | Compounded | Compounded | | Total | grew! | grew! | grew! | grew! | grew! | grew! | grew! | grew! | Your bank account will be doing a happy dance at the end of this eight-year savings marathon! --- Make sure to double-check your calculations and keep an eye on rounding errors in interest calculations, as they can lead to discrepancies in the final amount. Also, remember that keeping consistent and regular payments matter a lot in building your savings effectively!