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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Here are the solutions to the problems: 1. Calculate the balance accumulated: Step 1: Identify the given values for principal (P), interest rate (r), and time (t). P = R 3\,500 r = 7.5\% = 0.075 t = 2 years Step 2: Use the simple interest formula for the accumulated amount, A = P(1 + r · t). A = 3500(1 + 0.075 × 2) Step 3: Calculate the accumulated amount. A = 3500(1 + 0.15) A = 3500(1.15) A = R 4\,025 The balance accumulated is R 4\,025. 2. Calculate the accumulated amount: a) A loan of R 300 at a rate of 8% for 1 year. Step 1: Identify the given values. P = R 300 r = 8\% = 0.08 t = 1 year Step 2: Use the formula A = P(1 + r · t). A = 300(1 + 0.08 × 1) Step 3: Calculate the accumulated amount. A = 300(1 + 0.08) A = 300(1.08) A = R 324 The accumulated amount is R 324. b) An investment of R 2 250 at a rate of 12.5% p.a. for 6 years. Step 1: Identify the given values. P = R 2\,250 r = 12.5\% = 0.125 t = 6 years Step 2: Use the formula A = P(1 + r · t). A = 2250(1 + 0.125 × 6) Step 3: Calculate the accumulated amount. A = 2250(1 + 0.75) A = 2250(1.75) A = R 3\,937.50 The accumulated amount is R 3\,937.50. 3. Calculate the number of years: Step 1: Identify the given values for principal (P), accumulated amount (A), and interest rate (r). P = R 1\,000 A = R 2\,500 r = 8.2\% = 0.082 Step 2: Use the simple interest formula A = P(1 + r · t) and substitute the known values. 2500 = 1000(1 + 0.082 · t) Step 3: Solve for t. (2500)/(1000) = 1 + 0.082 · t 2.5 = 1 + 0.082 · t 2.5 - 1 = 0.082 · t 1.5 = 0.082 · t t = (1.5)/(0.082) t ≈ 18.29 years The number of years is approximately 18.29 years. 4. Calculate the interest rate: Step 1: Identify the given values for principal (P), accumulated amount (A), and time (t). The time period is from the son's 5th birthday to his 21st birthday. P = R 5\,000 A = R 18\,000 t = 21 - 5 = 16 years Step 2: Use the simple interest formula A = P(1 + r · t) and substitute the known values. 18000 = 5000(1 + r × 16) Step 3: Solve for r. (18000)/(5000) = 1 + 16r 3.6 = 1 + 16r 3.6 - 1 = 16r 2.6 = 16r r = (2.6)/(16) r = 0.1625 Step 4: Convert the rate to a percentage. r = 0.1625 × 100\% = 16.25\% The interest rate was 16.25\%. Send me the next one 📸