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
Welcome back — been a while! Let's pick up where you left off. 1. Calculate the future cost of the commodity. Step 1: Identify the given values. Initial cost P = M500 Inflation rate r = 10\% = 0.10 Time t = 5 years Step 2: Use the future value formula for inflation. FV = P(1 + r)^t Step 3: Substitute the values and calculate. FV = M500(1 + 0.10)^5 FV = M500(1.10)^5 FV = M500(1.61051) FV = M805.255 The commodity will cost M805.26 in 5 years. M805.26 2. Calculate the annual rate of compound interest. Step 1: Identify the given values. Initial amount P = M2,000 Future amount FV = M2,721 Time t = 4 years Step 2: Use the compound interest formula and solve for r. FV = P(1 + r)^t M2,721 = M2,000(1 + r)^4 Step 3: Isolate (1 + r)^4. (2,721)/(2,000) = (1 + r)^4 1.3605 = (1 + r)^4 Step 4: Take the fourth root of both sides. (1 + r) = (1.3605)^(1)/(4) (1 + r) ≈ 1.08 Step 5: Solve for r. r = 1.08 - 1 r = 0.08 r = 8\% The annual rate of compound interest is 8%. 8\% 3. Calculate the amount in Peo's account at different times. Initial deposit P = M3,500 Interest rates: r_1 = 3.7\% = 0.037 for the first 4 years r_2 = 4.2\% = 0.042 for the next 4 years (years 5-8) r_3 = 4.8\% = 0.048 for the final 2 years (years 9-10) a) after 3 years Step 1: Use the interest rate for the first 4 years (r_1 = 0.037). FV_3 = P(1 + r_1)^3 Step 2: Substitute the values and calculate. FV_3 = M3,500(1 + 0.037)^3 FV_3 = M3,500(1.037)^3 FV_3 = M3,500(1.115089) FV_3 = M3,902.81 After 3 years, the amount in the account is M3,902.81. M3,902.81 b) after 6 years Step 1: Calculate the amount after the first 4 years using r_1 = 0.037. FV_4 = M3,500(1 + 0.037)^4 FV_4 = M3,500(1.037)^4 FV_4 = M3,500(1.156319) FV_4 = M4,047.12 Step 2: Use FV_4 as the new principal and apply r_2 = 0.042 for the next 2 years (from year 4 to year 6). FV_6 = FV_4(1 + r_2)^2 FV_6 = M4,047.12(1 + 0.042)^2 FV_6 = M4,047.12(1.042)^2 FV_6 = M4,047.12(1.085764) FV_6 = M4,399.19 After 6 years, the amount in the account is M4,399.19. M4,399.19 c) after 10 years Step 1: Calculate the amount after the first 4 years using r_1 = 0.037. (Already calculated in part b) FV_4 = M4,047.12 Step 2: Calculate the amount after the next 4 years (total 8 years) using r_2 = 0.042. FV_8 = FV_4(1 + r_2)^4 FV_8 = M4,047.12(1 + 0.042)^4 FV_8 = M4,047.12(1.042)^4 FV_8 = M4,047.12(1.177176) FV_8 = M4,764.08 Step 3: Calculate the amount after the final 2 years (total 10 years) using r_3 = 0.048. FV_10 = FV_8(1 + r_3)^2 FV_10 = M4,764.08(1 + 0.048)^2 FV_10 = M4,764.08(1.048)^2 FV_10 = M4,764.08(1.098304) FV_10 = M5,232.06 After 10 years, the amount in the account is M5,232.06. M5,232.06 Send me the next one 📸