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. Question 4 Nolwazi wants to buy a new state of the art computer for R35 000. She decides to save by depositing an amount of R500 every month into an account carning \( 11,32 \% \) interest per year, compounded monthly. How many years (accurate to one decimal place) will it take Nolwazi to have R35 000 available?

Below are the step‐by‐step solutions for both questions. ─────────────────────────────── Question 3 We are given:  • Payment amount, P = R1 900 per week  • Annual interest rate = 9.7% compounded weekly  • Total time = 8 years Step 1. Determine the number of compounding periods:  Since interest is compounded weekly and there are 52 weeks in a year,   n = 8 × 52 = 416 weeks. Step 2. Calculate the periodic (weekly) interest rate:   i = 9.7%/52 = 0.097/52 ≈ 0.0018654 per week Step 3. Future value of an ordinary annuity:  Payments are made at the end of each period. The future value is given by   A = P × [((1 + i)ⁿ – 1) / i] Substitute the values:   A = 1900 × [((1 + 0.0018654)^(416) – 1) / 0.0018654] Let’s approximate (1 + 0.0018654)^(416). One way is to use logarithms:  ln(1.0018654) ≈ 0.001863, so   ln((1.0018654)^(416)) ≈ 416 × 0.001863 ≈ 0.775,  which gives   (1.0018654)^(416) ≈ e^(0.775) ≈ 2.17. Thus,  A ≈ 1900 × [(2.17 – 1) / 0.0018654]   = 1900 × (1.17 / 0.0018654)   ≈ 1900 × 627.9   ≈ R1,192,000 ─────────────────────────────── Timeline for Question 3  Time (in weeks) Action   Week 0 Start (initial balance = 0)   Week 1 Deposit R1 900 (end of first week)   Week 2 Deposit R1 900     ⋮   Week 415 Deposit R1 900   Week 416 Deposit R1 900 (last deposit)  After week 416 Account has accumulated interest on all deposits to ≈ R1,192,000 ─────────────────────────────── Question 4 We are given:  • Nolwazi must have R35 000 to buy the computer.  • She deposits R500 every month.  • Interest rate = 11.32% per year compounded monthly. Step 1. Determine the periodic (monthly) interest rate:   i = 11.32%/12 = 0.1132/12 ≈ 0.0094333 per month Step 2. Let n be the number of monthly deposits needed. The future value of an ordinary annuity is given by   A = P × [((1 + i)ⁿ – 1) / i] We set A = 35,000 and P = 500:   35,000 = 500 × [((1.0094333)ⁿ – 1) / 0.0094333] Solve for ((1.0094333)ⁿ – 1):   ((1.0094333)ⁿ – 1) = 35,000 × 0.0094333 / 500 Calculate the right‐side:   35,000/500 = 70, so   ((1.0094333)ⁿ – 1) = 70 × 0.0094333 ≈ 0.66 Thus,   (1.0094333)ⁿ ≈ 1 + 0.66 = 1.66 Step 3. Solve for n using logarithms:   n = ln(1.66) / ln(1.0094333) Calculate:   ln(1.66) ≈ 0.507 and ln(1.0094333) ≈ 0.00939,   n ≈ 0.507 / 0.00939 ≈ 54 Since n = 54 months, the number of years is:   54/12 = 4.5 years ─────────────────────────────── Final Answers Question 3: After 8 years (416 weeks) of depositing R1 900 each week into an account earning 9.7% per annum compounded weekly, the accumulated amount will be approximately R1,192,000. Question 4: Nolwazi needs to save for about 54 months, which is approximately 4.5 years, to have R35 000 in her account when depositing R500 every month at 11.32% per annum compounded monthly.