A bicycle repair shop sets up a savings fund to replace its diagnostic tools in future years. The fund grows by compound interest at a fixed rate of 4% per ...
Question 1 Report
A bicycle repair shop sets up a savings fund to replace its diagnostic tools in future years. The fund grows by compound interest at a fixed rate of 4% per year, compounded annually, and after 2 years the fund is worth £1352.
- Write down an expression, in terms of the original amount \(P\), for the value of the fund after 2 years. (2)
- Work out the value of \(P\), the amount originally invested. (2)
Answer Details
This question writes a general compound-interest expression and then uses a given final value to solve for the original principal.
Growing at \(4\%\) per year, compounded annually, for \(2\) years, the fund's value is:
\[P(1.04)^2\][2 marks]
Setting this equal to \(£1352\):
\[P(1.04)^2 = 1352\] \[P \times 1.0816 = 1352\] \[P = 1352 \div 1.0816 = £1250\][2 marks]
The original amount invested was \(£1250\). Dividing by the full two-year multiplier \(1.0816\) (rather than by \(1.08\), which would only reverse one year of interest) correctly undoes both years of compounding at once.
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