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 for questions 3, 4, 5, and 6. 3. Find the rate percent per annum simple interest for K420 to be the interest on K1200 invested for 5 years. Step 1: Identify the given values for simple interest. The formula for simple interest is I = P × R × T, where I is the interest, P is the principal, R is the annual interest rate, and T is the time in years. Given: Interest (I) = K420 Principal (P) = K1200 Time (T) = 5 years Step 2: Rearrange the formula to solve for the rate (R). R = (I)/(P × T) Step 3: Substitute the values and calculate the rate. R = K420K1200 × 5 R = (420)/(6000) R = 0.07 Step 4: Convert the decimal rate to a percentage. R = 0.07 × 100\% = 7\% 7\% per annum Refer to the given information to answer Questions 4 and 5 K8 000 is invested for 12 years at 12% pa. The interest is compounded half-yearly. 4. Calculate the amount after 12 years. Step 1: Identify the given values for compound interest. The formula for compound amount is A = P (1 + (R)/(n))^nt, where A is the amount, P is the principal, R is the annual interest rate, n is the number of times interest is compounded per year, and t is the time in years. Given: Principal (P) = K8 000 Annual interest rate (R) = 12% = 0.12 Time (t) = 12 years Compounding frequency (n) = 2 (half-yearly) Step 2: Calculate the values for (R)/(n) and nt. (R)/(n) = (0.12)/(2) = 0.06 nt = 2 × 12 = 24 Step 3: Substitute the values into the compound amount formula and calculate. A = K8000 (1 + 0.06)^24 A = K8000 (1.06)^24 A = K8000 × 4.048905 A = K32391.24 K32391.24 5. Calculate the interest earned after 12 years. Step 1: Use the amount calculated in Question 4 and the original principal. Amount (A) = K32391.24 Principal (P) = K8 000 Step 2: Subtract the principal from the amount to find the interest earned. Interest Earned = A - P Interest Earned = K32391.24 - K8000 Interest Earned = K24391.24 K24391.24 6. Evaluate: K5 000 (1 + 17\%)^5 = Step 1: Convert the percentage to a decimal and add it to 1. 1 + 17\% = 1 + 0.17 = 1.17 Step 2: Raise the result to the power of 5. (1.17)^5 ≈ 2.19245 Step 3: Multiply the result by K5 000. K5000 × 2.19245 K10962.25 K10962.25 Last free one today — make it count tomorrow, or type /upgrade for unlimited.