Mark Scheme
(a) Calculate the amount of money Benita would have at the end of 3 years. Give your answer correct to two decimal places. [3]
- Formula for compound interest:
\[
A = P \left(1 + \frac{r}{n}\right)^{nt}
\]
where:
- \( A \) = total amount
- \( P = 2500 \)
- \( r = 0.025 \) (annual interest rate)
- \( n = 12 \) (compounded monthly)
- \( t = 3 \) years
- Substitution: \[ A = 2500 \left(1 + \frac{0.025}{12}\right)^{12 \times 3} \]
- Intermediate calculation: \[ A = 2500 \left(1 + 0.0020833\right)^{36} \approx 2500 \times 1.07656 \approx 2691.40 \]
- Final answer: \( A \approx 2691.40 \).
- Correct working with substitutions and intermediate steps.
(b) Calculate the annual depreciation rate of the laptop. [3]
- Formula for depreciation:
\[
V = P(1 – r)^t
\]
where:
- \( V = 400 \) (value after depreciation)
- \( P = 2500 \) (initial cost)
- \( t = 3 \) years
- \( r \) = annual depreciation rate
- Substitution: \[ 400 = 2500(1 – r)^3 \]
- Rearranging: \[ (1 – r)^3 = \frac{400}{2500} = 0.16 \] Taking the cube root: \[ 1 – r = \sqrt[3]{0.16} \approx 0.5518 \]
- Depreciation rate: \[ r = 1 – 0.5518 \approx 0.4482 = 44.82\% \]
- Final answer: \( r \approx 44.82\% \).
- Correct working with logical steps.