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's how to calculate the total accumulated amount for Renita's investment under different compounding frequencies. The formula for compound interest is: A = P (1 + (r)/(n))^nt Where: A = accumulated amount P = principal amount (£25,000) r = annual interest rate (12% or 0.12) n = number of times interest is compounded per year t = number of years (4 years) 1) Annually Step 1: Identify the values for annual compounding. For annual compounding, n=1. P = 25,000 r = 0.12 n = 1 t = 4 Step 2: Substitute the values into the compound interest formula and calculate. A = 25000 (1 + (0.12)/(1))^1 × 4 A = 25000 (1.12)^4 A = 25000 × 1.57351936 A = 39337.98 The total amount accumulated annually is £39337.98. 2) Monthly Step 1: Identify the values for monthly compounding. For monthly compounding, n=12. P = 25,000 r = 0.12 n = 12 t = 4 Step 2: Substitute the values into the compound interest formula and calculate. A = 25000 (1 + (0.12)/(12))^12 × 4 A = 25000 (1 + 0.01)^48 A = 25000 (1.01)^48 A = 25000 × 1.61222607768 A = 40305.65 The total amount accumulated monthly is £40305.65. 3) Half-yearly Step 1: Identify the values for half-yearly compounding. For half-yearly compounding, n=2. P = 25,000 r = 0.12 n = 2 t = 4 Step 2: Substitute the values into the compound interest formula and calculate. A = 25000 (1 + (0.12)/(2))^2 × 4 A = 25000 (1 + 0.06)^8 A = 25000 (1.06)^8 A = 25000 × 1.5938480745 A = 39846.20 The total amount accumulated half-yearly is £39846.20. 4) Quarterly Step 1: Identify the values for quarterly compounding. For quarterly compounding, n=4. P = 25,000 r = 0.12 n = 4 t = 4 Step 2: Substitute the values into the compound interest formula and calculate. A = 25000 (1 + (0.12)/(4))^4 × 4 A = 25000 (1 + 0.03)^16 A = 25000 (1.03)^16 A = 25000 × 1.6047064441 A = 40117.66 The total amount accumulated quarterly is £40117.66. Send me the next one 📸