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.

Answered by Maths tutor

3453 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

How many books and modules and what are they all about?


solve dy/dx = y(sec x)^2


Find and classify all the stationary points of the function f(x) = x^3 - 3x^2 + 8


C4 June 2014 Q4: Water is flowing into a vase. When the depth of water is h cm, the volume of water V cm^3 is given by V=4πh(h+4). Water flows into the vase at a constant rate of 80π cm^3/s. Find the rate of change of the depth of water in cm/s, when h=6.


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

MyTutor is part of the IXL family of brands:

© 2025 by IXL Learning