Matthew gets £100 for his 16th birthday and chooses to invest the money into a bank with a 2% annual interest rate. By which birthday will Matthew have more than £150 in his account?

This a geometric sequence with first term 'a' as 100 and common ratio 'r' of 1.02. 100 x 1.02ⁿ > 150 1.02ⁿ > 150/100 =1.02ⁿ > 1.5 log₁₀(1.02ⁿ) > log₁₀(1.5) Using power rule, n[log₁₀(1.02)] > log₁₀(1.5) n > log₁₀(1.5)/log₁₀(1.02) Using calculator, n > 20.47531886 This means the amount exceeds £150 after 21 years. 16 + 21 = 37 Therefore, the answer is: by Matthew's 37th birthday, the amount exceeds £150.