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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You're on a roll — let's tackle these finance problems. Simple Interest 1. Lisa's investment Step 1: Identify the principal amount (P), interest rate (i), and time (n). P = R5\,000 i = 7.5\% = 0.075 per year n = 6 years Step 2: Calculate the simple interest earned using the formula I = P · i · n. I = R5\,000 × 0.075 × 6 I = R2\,250 Step 3: Calculate the total value of the investment (A) by adding the principal and the interest. A = P + I A = R5\,000 + R2\,250 A = R7\,250 The value of Lisa's investment at the end of 6 years is R7 250.00. 2. Jack's car purchase Step 1: Identify the selling price of the car. Selling Price = R120 000 Step 2: Calculate the deposit amount (20% of the selling price). Deposit = R120\,000 × 0.20 Deposit = R24\,000 Step 3: Calculate the loan amount (principal P) after the deposit. Loan Amount = Selling Price - Deposit Loan Amount = R120\,000 - R24\,000 Loan Amount = R96\,000 Step 4: Calculate the simple interest on the loan amount. P = R96\,000 i = 10.5\% = 0.105 per year n = 5 years I = P · i · n I = R96\,000 × 0.105 × 5 I = R50\,400 Step 5: Calculate the total amount Jack pays for the car (Deposit + Loan Amount + Interest on Loan). Total Paid = Deposit + Loan Amount + Interest on Loan Total Paid = R24\,000 + R96\,000 + R50\,400 Total Paid = R170\,400 The total amount Jack pays for the car is R170 400.00. Compound Interest 1. R130 000 investment P = R130\,000 Annual interest rate = 12% = 0.12 Time (n) = 3 years Compounded annually. a) Calculate the total interest earned. Step 1: Calculate the future value (A) using the compound interest formula A = P(1 + i)^n. A = R130\,000(1 + 0.12)^3 A = R130\,000(1.12)^3 A = R130\,000 × 1.404928 A = R182\,640.64 Step 2: Calculate the total interest earned (I = A - P). I = R182\,640.64 - R130\,000 I = R52\,640.64 The total interest earned is R52 640.64. b) Determine the value of the investment after three years. The value of the investment after three years is the future value calculated in part (a). The value of the investment after three years is R182 640.64. 2. Jason's R400 000 investment P = R400\,000 Time = 1.5 years Annual interest rate = 10% = 0.10 Compounded quarterly. a) Determine the value of the investment after 1.5 years. Step 1: Determine the interest rate per compounding period (i) and the total number of compounding periods (n). Since it's compounded quarterly, there are 4 compounding periods per year. i = Annual RateNumber of Compounding Periods per Year = (0.10)/(4) = 0.025 n = Years × Number of Compounding Periods per Year = 1.5 × 4 = 6 periods Step 2: Calculate the future value (A) using the compound interest formula A = P(1 + i)^n. A = R400\,000(1 + 0.025)^6 A = R400\,000(1.025)^6 A = R400\,000 × 1.159693418 A = R463\,877.37 The value of the investment after 1.5 years is R463 877.37. b) What is the total amount of interest earned? Step 1: Calculate the total interest earned (I = A - P). I = R463\,877.37 - R400\,000 I = R63\,877.37 The total amount of interest earned is R63 877.37. Send me the next one 📸