This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
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5.1.1 Calculate the book value of the printer at the end of the 5 year period. Step 1: Use the reducing balance depreciation formula. The formula for depreciation on a reducing balance is A = P(1 - i)^n, where A is the book value, P is the initial cost, i is the depreciation rate, and n is the number of years. A = R250\,000(1 - 0.10)^5 Step 2: Calculate the book value. A = R250\,000(0.90)^5 A = R250\,000(0.59049) A = R147\,622.50 The book value of the printer at the end of 5 years is R147 622.50. 5.1.2 Calculate the cost of a similar printer when the 5 year period expires. Step 1: Use the compound interest formula for inflation. The formula for future value with inflation is A = P(1 + i)^n, where A is the future cost, P is the current cost, i is the inflation rate, and n is the number of years. A = R250\,000(1 + 0.08)^5 Step 2: Calculate the future cost. A = R250\,000(1.08)^5 A = R250\,000(1.4693280768) A = R367\,332.02 The cost of a similar printer after 5 years is R367 332.02. 5.1.3 Calculate the amount of money that must be saved in order to have enough money to replace the printer in 5 years. Step 1: Calculate the selling price of the used printer. The school sells the used printer for 95% of its book value (from 5.1.1). Selling Price = 0.95 × R147\,622.50 Selling Price = R140\,241.38 Step 2: Calculate the amount to be saved. The amount to be saved is the cost of the new printer (from 5.1.2) minus the selling price of the old printer. Amount to be Saved = R367\,332.02 - R140\,241.38 Amount to be Saved = R227\,090.64 The amount of money that must be saved is R227 090.64. 5.2.1 Determine which bank offers the best interest rate. Step 1: State the effective interest rate for Bank A. Bank A offers an effective interest rate of 12\% per annum. Step 2: Calculate the effective interest rate for Bank B. Bank B offers a nominal interest rate of 11.5\% p.a., compounded monthly. The formula for the effective annual rate is i_eff = (1 + i_nomm)^m - 1. Here, i_nom = 0.115 and m = 12. i_eff = (1 + (0.115)/(12))^12 - 1 i_eff = (1 + 0.0095833333)^12 - 1 i_eff = (1.0095833333)^12 - 1 i_eff = 1.121339 - 1 i_eff = 0.121339 i_eff = 12.13\% Step 3: Compare the effective interest rates. Bank A effective rate: 12\% Bank B effective rate: 12.13\% Since 12.13\% > 12\%, Bank B offers a better interest rate. Bank B offers the best interest rate. Send me the next one 📸