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
a) i) To calculate the present value of the annuity, we use the formula for the present value of an ordinary annuity (PVA) when the Present Value Interest Factor of an Annuity (PVIFA) is given. Step 1: Identify the given values. Annuity payment, A = N500,000 Present Value Interest Factor of an Annuity (PVIFA) = 21.7243 Step 2: Apply the formula for Present Value of an Annuity. PVA = A × PVIFA Step 3: Substitute the values and calculate the Present Value. PVA = N500,000 × 21.7243 PVA = N10,862,150 The present value is N10,862,150. a) ii) To find the interest rate 'i', we use the Future Value of an Annuity formula, as indicated by the expression ((1+i)^n - 1)/(i). Step 1: Identify the given values and the formula. Future Value, FV = N2,520,000.00 Annuity Payment, A = N1,200,000.00 Number of years, n = 2 The formula for Future Value of an Annuity is FV = A × ((1+i)^n - 1)/(i). Step 2: Substitute the given values into the formula. N2,520,000.00 = N1,200,000.00 × ((1+i)^2 - 1)/(i) Step 3: Isolate the Future Value Interest Factor of an Annuity (FVIFA) term. (N2,520,000.00)/(N1,200,000.00) = ((1+i)^2 - 1)/(i) 2.1 = ((1+i)^2 - 1)/(i) Step 4: Expand the numerator and simplify the equation. We know that (1+i)^2 - 1 = (1 + 2i + i^2) - 1 = 2i + i^2. So, the equation becomes: 2.1 = (2i + i^2)/(i) Since i cannot be zero for an interest rate, we can divide the numerator by i: 2.1 = 2 + i Step 5: Solve for i. i = 2.1 - 2 i = 0.1 Step 6: Convert the decimal interest rate to a percentage. i = 0.1 × 100\% = 10\% The interest rate is 10\%. Send me the next one 📸