Northern Bank has two types of account - Edexcel - GCSE Maths - Question 5 - 2018 - Paper 2

To find out who gets the most interest after 3 years, we will calculate the compound interest for both accounts using the formula:

$A = P(1 + r)^n$

where:

• $A$ = the amount of money accumulated after n years, including interest.
• $P$ = principal amount (the initial amount of money).
• $r$ = annual interest rate (decimal).
• $n$ = number of years the money is invested.

For Ali's cash savings account:

• Principal ($P$) = £2000
• Interest rate ($r$) = 2.5% = 0.025
• Number of years ($n$) = 3

Calculating: $A_{cash} = 2000(1 + 0.025)^3$ $= 2000(1.025)^3$ $= 2000(1.0769)$ $= £2153.85$

For Ben's shares account:

• Principal ($P$) = £1600
• Interest rate ($r$) = 3.5% = 0.035 for the first 2 years, then 4% = 0.04 for the 3rd year.

Calculating for first 2 years: $A_{shares,2} = 1600(1 + 0.035)^2$ $= 1600(1.035)^2$ $= 1600(1.071225)$ $= £1714.00$

Now, for the 3rd year at 4%: $A_{shares,3} = 1714(1 + 0.04)$ $= 1714(1.04)$ $= £1788.56$

Thus, after 3 years:

• Ali (cash savings) = £2153.85
• Ben (shares) = £1788.56

Conclusion: Ali will receive £2153.85 which is more than Ben’s £1788.56.