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 — here are the solutions for Question 4 and Question 5. Question 4 Given: Principal (P) = 5000 Amount (A) = 5810 Time (T) = 3 years i) The simple interest earned Step 1: Calculate the simple interest (I) by subtracting the principal from the amount. I = A - P I = \5810 - \5000 I = \810 The simple interest earned is \810. ii) The annual interest rate paid by the credit union Step 1: Use the simple interest formula I = P × R × T to find the rate (R). R = (I)/(P × T) R = (\810)/(\5000 × 3 years) R = (\810)/(\15000) Step 2: Convert the decimal rate to a percentage. R = 0.054 R = 0.054 × 100\% = 5.4\% The annual interest rate is 5.4\%. iii) The length of time it will take for Mr Adams' investment to be doubled, at the same rate of interest. Step 1: Determine the amount needed for the investment to be doubled. Doubled amount = 2 × P = 2 × \5000 = \10000 Step 2: Calculate the interest needed to double the investment. I = Doubled amount - P = \10000 - \5000 = \5000 Step 3: Use the simple interest formula I = P × R × T to find the time (T), using the rate R = 0.054 from part (ii). T = (I)/(P × R) T = (\5000)/(\5000 × 0.054) T = (1)/(0.054) T ≈ 18.5185 years The length of time it will take for the investment to be doubled is approximately 18.52 years (rounded to two decimal places). Question 5 i) If a washing machine was sold for 3960 during the promotion, what was the cost price? Given: Selling Price (SP) = 3960 Profit percentage = 12.5% Step 1: Let the Cost Price (CP) be X. The selling price is the cost price plus 12.5% profit. SP = CP + (Profit percentage × CP) \3960 = X + (0.125 × X) \3960 = X(1 + 0.125) \3960 = 1.125X Step 2: Solve for X. X = (\3960)/(1.125) X = \3520 The cost price was \3520. ii) During the Summer Sale, the washing machine's selling price was then reduced by 15% of the Easter sale price. What was the percentage profit or loss during the Summer Sale relative to the cost price? Given: Easter sale price (SP_Easter) = 3960 (from part i) Cost Price (CP) = 3520 (from part i) Reduction in Summer Sale = 15% of Easter sale price Step 1: Calculate the Summer Sale price (SP_Summer). SP\_Summer = SP\_Easter - (0.15 × SP\_Easter) SP\_Summer = \3960 - (0.15 × \3960) SP\_Summer = \3960 - \594 SP\_Summer = \3366 Step 2: Calculate the profit or loss during the Summer Sale. Profit/Loss = SP\_Summer - CP Profit/Loss = \3366 - \3520 Profit/Loss = -\154 Since the result is negative, it is a loss of 154. Step 3: Calculate the percentage profit or loss relative to the cost price. Percentage Profit/Loss = ( Profit/LossCP ) × 100\% Percentage Profit/Loss = ( (-\154)/(\3520) ) × 100\% Percentage Profit/Loss = -0.04375 × 100\% Percentage Profit/Loss = -4.375\% There was a 4.375\% loss during the Summer Sale relative to the cost price. What's next?