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
Here's the solution to question 1. Given: Principal (P) = N250000 Interest rate (r) = 15% = 0.15 Time (t) = 15 years a) Simple interest The formula for simple interest is A = P(1 + rt). Step 1: Substitute the given values into the formula. A = 250000(1 + 0.15 × 15) Step 2: Calculate the product of r and t. A = 250000(1 + 2.25) Step 3: Add the values inside the parenthesis. A = 250000(3.25) Step 4: Multiply to find the final amount. A = 812500 The amount after 15 years with simple interest is N812500.00. b) Interest compounded: The formula for compound interest compounded n times per year is A = P(1 + (r)/(n))^nt. The formula for compound interest compounded continuously is A = Pe^rt. i. annually For annual compounding, n=1. Step 1: Substitute the values into the formula. A = 250000(1 + (0.15)/(1))^1 × 15 A = 250000(1.15)^15 Step 2: Calculate (1.15)^15. A = 250000 × 8.1370619 Step 3: Multiply to find the final amount. A = 2034265.475 The amount after 15 years compounded annually is N2034265.48. ii. quarterly For quarterly compounding, n=4. Step 1: Substitute the values into the formula. A = 250000(1 + (0.15)/(4))^4 × 15 A = 250000(1 + 0.0375)^60 A = 250000(1.0375)^60 Step 2: Calculate (1.0375)^60. A = 250000 × 9.429007 Step 3: Multiply to find the final amount. A = 2357251.75 The amount after 15 years compounded quarterly is N2357251.75. iii. semi-annually For semi-annual compounding, n=2. Step 1: Substitute the values into the formula. A = 250000(1 + (0.15)/(2))^2 × 15 A = 250000(1 + 0.075)^30 A = 250000(1.075)^30 Step 2: Calculate (1.075)^30. A = 250000 × 8.75699 Step 3: Multiply to find the final amount. A = 2189247.5 The amount after 15 years compounded semi-annually is N2189247.50. iv. continuously For continuous compounding, the formula is A = Pe^rt. Step 1: Substitute the values into the formula. A = 250000 × e^0.15 × 15 A = 250000 × e^2.25 Step 2: Calculate e^2.25. A = 250000 × 9.487735 Step 3: Multiply to find the final amount. A = 2371933.75 The amount after 15 years compounded continuously is N2371933.75. 3 done, 2 left today. You're making progress.