Lewis saves KSh 200 at the beginning of each month for 12 months. If the bank offers a simple interest rate of 1/4% per annum, calculate the total interest earned by December.

Step 1: Identify the given information. The principal amount saved each month, P = KSh 200. The annual simple interest rate, R = (1)/(4)\% = 0.25\%. The period of saving is from January 2018 to December 2018, which is 12 months. The formula for simple interest is I = (P × R × T)/(100), where T is the time in years. Step 2: Determine the time (in years) for which each monthly deposit earns interest. Lewis saves KSh 200 at the beginning of each month. The January deposit earns interest for 12 months (T = (12)/(12) years). The February deposit earns interest for 11 months (T = (11)/(12) years). The March deposit earns interest for 10 months (T = (10)/(12) years). ... The December deposit earns interest for 1 month (T = (1)/(12) years). Step 3: Calculate the total interest earned. The total interest is the sum of the interest earned by each monthly deposit. I_total = (200 × 0.25 × 12)/(12)100 + (200 × 0.25 × 11)/(12)100 + + (200 × 0.25 × 1)/(12)100 Factor out the common terms: I_total = (200 × 0.25)/(100) × ( (12)/(12) + (11)/(12) + + (1)/(12) ) I_total = (50)/(100) × (1)/(12) × (12 + 11 + + 1) I_total = 0.5 × (1)/(12) × (12 + 11 + + 1) Step 4: Sum the series and calculate the total interest. The sum of the first 12 natural numbers is given by the formula (n(n+1))/(2). For n=12: 12 + 11 + + 1 = (12(12+1))/(2) = (12 × 13)/(2) = 6 × 13 = 78 Substitute this sum back into the total interest equation: I_total = 0.5 × (1)/(12) × 78 I_total = (0.5 × 78)/(12) I_total = (39)/(12) I_total = (13)/(4) I_total = 3.25 The total interest received during the 12 months is KSh 3.25. KSh 3.25 Last free one today — make it count tomorrow, or type /upgrade for unlimited.