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.
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