Calculations In Everyday Contexts.

Wage Rises Example 1. A computer operator earning £16152 per annum is given a wage rise of £2400. Calculate : (a) The new annual wage. (b) The new monthly wage. Solution (a) The new annual wage = old wage + pay rise. = 16 152 + 2400 = £18 552 per annum. (b) Monthly salary = annual salary  12 months = £18 552  12 = £1546 per month

Example 2. Jane earns £18564 per year. She is given a 7 % pay rise but is still paid weekly. What does Jane earn per week? Solution. Calculate Jane’s pay rise: 7 % of £18 564 = 0.07 x £18 564 = £1299.48 New wage = 18 564 + 1 299.48 = £ 19 863.48 For a weekly wage divide by 52 Weekly wage = 19 863 . 48  52 = £381.99 per week.

Commission Example 1. Sam is paid a basic wage of £450 a month and 3.5% commission on sales he makes. Calculate his total salary in a month when he sold £45 000 worth of goods. Solution. Commission = 3.5% of 45 000 = 0.035 x 45 000 = £1575 Total wage = basic + commission = 450 + 1575 = £ 2025

Example 2. Emily is paid a basic wage of £ 678 per month and 7.5% commission on sales she makes over the value of £20 000. Calculate her total salary in a month when she sells £47 500 worth of goods. Solution. Amount of sales commission is paid on = 47 500 – 20 000 = £27 500 Amount of commission = £27 500 x 0.075 = £2062.50 Total salary = basic + commission = 678 + 2062.50 = £2740.50

Overtime & Bonuses. Example 1. If John’s normal wage was £8.60 an hour , calculate his wage at : (a) Double time (b) Time and a half. Solution (a) Double time = 2 x normal wage = 2 x 8.60 = £17.20 (b) Time and a half = normal wage plus half as much again. = 8.60 + 4.30 = £12.90

Example 2. Billy is paid £20.40 an hour for a 35 hour week and time and a half for any overtime he does. Calculate his wage in a week when he worked 43 hours . Solution. Normal wage = 20.40 x 35 = £714 Overtime worked = 43 – 35 = 8 hours Overtime pay = 20.40 + 10.20 = £30.60 Overtime wage = 30.60 x 8 = £244.80 Total wages = 714 + 244.80 = £958.80

Hire Purchase. Example 1. I buy a bike on Hire Purchase (H.P) for a deposit of £20 and 12 monthly payments of £14.50.Calculate the total H.P price. Solution. H.P cost = Deposit + Monthly Payments. Monthly Payments = 12 x 14.50 = £174 H.P price = 20 + 174 = £194

Example 2. A television costs £350 cash price. It can be bought on H.P for a deposit of 10% of the cash price and 2 years of monthly payments of £17.50. Calculate the difference between the cash price and the H.P price. Solution Deposit = 10% of 350 = £35 Monthly payments = 24 x 17.50 = £420 Total H.P price = 35 + 420 = £455 Difference in price = H.P – C.P = 455 - 350 = £105

Example 3. A car with a cash price of £ 8 500 can be bought on H.P for a 15% deposit and a monthly payment of £210 for 3 years. Calculate the total H.P costs. Solution. Cost of deposit: 15% of 8500 = £1275 Monthly payments 3 years = 36 months. 210 x 36 = £7560 Total H.P price: £1275 + £7560 = £8 835

Insurance Premiums. Example 1. How much would a £240 000 house cost to ensure if the insurance company charges £2.76 per £1000 insured ? Solution. £1000 worth of insurance = £2.76 £240 000 worth of insurance = 2.76 x 240 = £662.40

Example 2. How much would a house worth £185 000 with contents valued at £80 000 be to insure if the buildings premium was £2.32 per £1000 and contents premium £1.54 per £1000 ? Solution. House insurance: 2.32 x 185 = £429.20 Contents insurance: 1.54 x 80 = £123.20 Total insurance costs : £429.20 + £123.20 = £552.40