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 are the solutions for Question 3: Question 3: Initial deposit (P) = M3,500 Interest rates: First 4 years: r_1 = 3.7\% = 0.037 Next 4 years (years 5-8): r_2 = 4.2\% = 0.042 Final 2 years (years 9-10): r_3 = 4.8\% = 0.048 a) after 3 years Step 1: Identify the values for the first period. P = M3,500 r_1 = 0.037 t = 3 years Step 2: Use the compound interest formula. FV = P(1 + r_1)^t Step 3: Substitute the values and calculate. FV = M3,500(1 + 0.037)^3 FV = M3,500(1.037)^3 FV = M3,500 × 1.114789 FV = M3,901.76 After 3 years, the amount in Peo's account will be M3,901.76. b) after 6 years Step 1: Calculate the amount after the first 4 years. P_1 = M3,500 r_1 = 0.037 t_1 = 4 years FV_1 = P_1(1 + r_1)^t_1 FV_1 = M3,500(1 + 0.037)^4 FV_1 = M3,500(1.037)^4 FV_1 = M3,500 × 1.155919 FV_1 = M4,045.72 Step 2: Use FV_1 as the new principal for the next period. The next period is for 6 - 4 = 2 years at r_2 = 0.042. P_2 = M4,045.72 r_2 = 0.042 t_2 = 2 years FV_2 = P_2(1 + r_2)^t_2 FV_2 = M4,045.72(1 + 0.042)^2 FV_2 = M4,045.72(1.042)^2 FV_2 = M4,045.72 × 1.085764 FV_2 = M4,394.02 After 6 years, the amount in Peo's account will be M4,394.02. c) after 10 years Step 1: Calculate the amount after the first 4 years (from part b). FV_1 = M4,045.72 Step 2: Calculate the amount after the next 4 years (total 8 years). P_2 = FV_1 = M4,045.72 r_2 = 0.042 t_2 = 4 years FV_2 = P_2(1 + r_2)^t_2 FV_2 = M4,045.72(1 + 0.042)^4 FV_2 = M4,045.72(1.042)^4 FV_2 = M4,045.72 × 1.177216 FV_2 = M4,763.45 Step 3: Calculate the amount after the final 2 years (total 10 years). P_3 = FV_2 = M4,763.45 r_3 = 0.048 t_3 = 2 years FV_3 = P_3(1 + r_3)^t_3 FV_3 = M4,763.45(1 + 0.048)^2 FV_3 = M4,763.45(1.048)^2 FV_3 = M4,763.45 × 1.098304 FV_3 = M5,231.97 After 10 years, the amount in Peo's account will be M5,231.97. Last free one today — make it count tomorrow, or type /upgrade for unlimited.