Derek buys a house for €150,000. He sells the house for €154,500. (a) Work out Derek's percentage profit. (b) Derek invests €154,500 for 2 years at 4% per year compound interest. Work out the value of the investment at the end of 2 years.

Answer

(a) To calculate Derek's percentage profit, we first find the profit amount. The profit is calculated as follows: Profit = Selling Price - Cost Price Profit = €154,500 - €150,000 = €4,500 Next, to find the percentage profit, we use the formula: Percentage Profit = (Profit / Cost Price) x 100% Percentage Profit = (€4,500 / €150,000) x 100% = 3% Thus, Derek's percentage profit is 3%. (b) For the compound interest calculation, we use the formula for compound interest: A = P(1 + r/n)^(nt) Where: A = the future value of the investment/loan, including interest P = the principal investment amount (€154,500) r = the annual interest rate (decimal) (4% = 0.04)\nn = the number of times that interest is compounded per year (1 for yearly) t = the number of years the money is invested (2 years) Plugging in the values: A = 154500(1 + 0.04/1)^(1*2) A = 154500(1 + 0.04)^(2) A = 154500(1.04)^(2) A = 154500(1.0816) A ≈ €166,220.20 Thus, the value of the investment at the end of 2 years is approximately €166,220.20.