IBDP Maths SL 1.4 Financial applications AA HL Paper 2- Exam Style Questions- New Syllabus
Question
(a) Calculate the value of the vehicle after a period of ten years. Provide your result rounded to two decimal places.
(b) Determine the minimum number of months required for the real value of this investment to exceed €55,000.
Syllabus Topic Codes (IB Mathematics AA HL):
▶️ Answer/Explanation
(a)
The depreciation factor per year is \( 1 – 0.15 = 0.85 \).
Value after 10 years: \( 30000 \times (0.85)^{10} \approx 5906.232130 \).
Answer: €5906.23.
(b)
To find the real monthly growth rate, we adjust the nominal interest for inflation:
\( r_{real} = \frac{1 + \text{interest rate}}{1 + \text{inflation rate}} – 1 = \frac{1.015}{1.008} – 1 \approx 0.006944 \dots \)
We need the real value to exceed €55,000:
\( 50000(1.006944)^n > 55000 \)
\( (1.006944)^n > 1.1 \)
Taking logs: \( n \ln(1.006944) > \ln(1.1) \)
\( n > \frac{\ln(1.1)}{\ln(1.006944)} \approx 13.772 \).
Since \( n \) represents a whole number of months, we round up.
Answer: 14 months.