Standard +0.3 This is a straightforward compound interest comparison requiring students to set up two exponential expressions (P(1.01)^n vs P(1.05)(1.006)^(n-1)) and solve the inequality algebraically using logarithms. While it involves multiple steps and logarithmic manipulation, it's a standard application question with clear structure and no novel insight required—slightly easier than average for A-level.
Robert wants to deposit \(£P\) into a savings account. He has a choice of two accounts.
• Account \(A\) offers an annual compound interest rate of \(1\%\).
• Account \(B\) offers an interest rate of \(5\%\) for the first year and an annual compound interest rate of \(0.6\%\) for each subsequent year.
After \(n\) years, account \(A\) is more profitable than account \(B\). Find the smallest value of \(n\). [5]
Write the question number(s) in the left-hand margin.
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Answer
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number
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Write the question number(s) in the left-hand margin.
Question 15:
15 | 5
Total | 120
Question
number | Additional page, if required.
Write the question number(s) in the left-hand margin.
Question
number | Additional page, if required.
Write the question number(s) in the left-hand margin.
Robert wants to deposit $£P$ into a savings account. He has a choice of two accounts.
• Account $A$ offers an annual compound interest rate of $1\%$.
• Account $B$ offers an interest rate of $5\%$ for the first year and an annual compound interest rate of $0.6\%$ for each subsequent year.
After $n$ years, account $A$ is more profitable than account $B$. Find the smallest value of $n$. [5]
\hfill \mbox{\textit{WJEC Unit 3 2024 Q15 [5]}}