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
You're on a roll — Step 1: Solve part (c)(i). This question involves simple interest. The formula for simple interest is I = PRT, where: • I is the total interest earned. • P is the principal amount (initial investment). • R is the annual interest rate (as a decimal). • T is the time in years. Given: • P = \500 • R = 1.7\% = 0.017 • T = 10 years Substitute these values into the formula: I = \500 × 0.017 × 10 I = \85 Step 2: Solve part (c)(ii). This question involves compound interest, compounded daily. The formula for compound interest is A = P(1 + (r)/(n))^nt, where: • A is the final amount. • P is the principal amount (initial investment). • r is the annual interest rate (as a decimal). • n is the number of times interest is compounded per year. • t is the time in years. Given: • P = \200 • Daily interest rate = 0.0035\% • Time = 1 year = 365 days First, convert the daily interest rate to a decimal: Daily rate = 0.0035\% = (0.0035)/(100) = 0.000035 Since the interest is compounded daily, the number of compounding periods is n = 365 (days in 1 year). The interest rate given is already a per-day rate, so we can use it directly in the compound interest formula where r/n becomes the daily rate and nt becomes the total number of days. Let i_day be the daily interest rate. The formula simplifies to A = P(1 + i_day)^number of days. Substitute the values: A = \200 (1 + 0.000035)^365 A = \200 (1.000035)^365 Calculate the value inside the parenthesis: (1.000035)^365 ≈ 1.01285 Now, multiply by the principal: A = \200 × 1.01285 A ≈ \202.57 c) i) The total interest earned is \85. ii) The value of Ollie's investment at the end of 1 year is \202.57. Just one more to go! Send it over.