An investment of GHS 10,000 is being considered for two options. Option A offers an 8% annual interest rate compounded quarterly. Option B offers a 7.5% annual interest rate compounded monthly. Both i

Step 1: Calculate the final amount for Option A. The formula for compound interest is A = P (1 + (r)/(n))^nt. For Option A: P = GHS 10,000 r = 8\% = 0.08 n = 4 (compounded quarterly) t = 5 years A_A = 10000 (1 + (0.08)/(4))^4 × 5 A_A = 10000 (1 + 0.02)^20 A_A = 10000 (1.02)^20 A_A = 10000 × 1.4859473959 A_A = 14859.47 The final amount for Option A is GHS 14859.47. Step 2: Calculate the final amount for Option B. For Option B: P = GHS 10,000 r = 7.5\% = 0.075 n = 12 (compounded monthly) t = 5 years A_B = 10000 (1 + (0.075)/(12))^12 × 5 A_B = 10000 (1 + 0.00625)^60 A_B = 10000 (1.00625)^60 A_B = 10000 × 1.449948408 A_B = 14499.48 The final amount for Option B is GHS 14499.48. Step 3: Determine which option yields more profit and by how much. Profit for Option A = Final Amount - Principal P_A = 14859.47 - 10000 = 4859.47 Profit for Option B = Final Amount - Principal P_B = 14499.48 - 10000 = 4499.48 Option A yields more profit. Difference in profit = P_A - P_B = 4859.47 - 4499.48 = 359.99 Option A yields more profit by GHS 359.99. Step 4: Calculate the time for the investment to double under Option A. The formula given is t = ((2))/(n (1+r)n). For Option A: r = 0.08 n = 4 t = ((2))/(4 (1+0.08)4) t = ((2))/(4 (1.02)) t = (0.693147)/(4 × 0.0198026) t = (0.693147)/(0.0792104) t = 8.7506 It would take approximately 8.75 years for the investment to double. Step 5: Discuss the relationship between compounding frequency and final amount. Generally, for a given principal, annual interest rate, and time period, a higher compounding frequency (more times per year) leads to a higher final amount. This is because interest is calculated and added to the principal more often, allowing subsequent interest calculations to be based on a larger principal, leading to greater overall growth. Send me the next one 📸