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.
ScanSolve AI Answer
To solve this problem, the principal amount, interest rate, and time period for Option 2 are required. This information is not visible in the provided image. Therefore, I will make the following assumptions to demonstrate the calculation: Principal amount (P) = R10\,000 Annual interest rate (i) = 8\% or 0.08 Number of years (n) = 5 b) Calculate the total amount that must be repaid if you choose Option 2 (compound interest). Step 1: Write down the compound interest formula. The formula for the total amount (A) with compound interest is: A = P(1 + i)^n where P is the principal amount, i is the annual interest rate, and n is the number of years. Step 2: Substitute the assumed values into the formula. A = 10\,000(1 + 0.08)^5 Step 3: Calculate the total amount. A = 10\,000(1.08)^5 A = 10\,000(1.4693280768) A = R14\,693.28 The total amount to be repaid for Option 2 is R14\,693.28. c) Compare the two options and justify which repayment option is cheaper. To compare the options, we need the total repayment amount for Option 1. Since this is not provided, I will assume Option 1 is a simple interest loan with the same principal, rate, and time as assumed for Option 2. Step 1: Calculate the total amount for Option 1 (Simple Interest, based on assumptions). Assumptions: P = R10\,000, r = 8\% = 0.08, t = 5 years. The formula for simple interest total amount (A_1) is: A_1 = P(1 + rt) A_1 = 10\,000(1 + 0.08 × 5) A_1 = 10\,000(1 + 0.40) A_1 = 10\,000(1.40) A_1 = R14\,000 Step 2: Compare the total amounts for Option 1 and Option 2. Total for Option 1: R14\,000 Total for Option 2: R14\,693.28 Step 3: Justify which option is cheaper. Comparing the two amounts, R14\,000 < R14\,693.28. Therefore, Option 1 is cheaper. This is because simple interest calculates interest only on the principal amount, whereas compound interest calculates interest on the principal and also on the accumulated interest from previous periods, leading to a higher total repayment over time. Send me the next one 📸