IBDP Maths MAA SL 1.4 Financial applications HL Paper 1- Exam Style Questions
Question
Most-appropriate topic codes (IB Mathematics Analysis and Approaches 2021):
• SL 1.9: The binomial theorem: expansion of \( (a + b)^n \), \( n \in \mathbb{N} \) — part (b)
▶️ Answer/Explanation
(a) Determining \( k \):
Nominal annual interest rate = 4% = 0.04
Compounded quarterly ⇒ interest rate per quarter = \( \frac{0.04}{4} = 0.01 \)
Thus \( k = 0.01 \) or \( \frac{1}{100} \).
\( \boxed{k = 0.01} \)
(b) Expanding \( (1 + x)^4 \):
Using the binomial theorem:
\( (1 + x)^4 = 1 + 4x + 6x^2 + 4x^3 + x^4 \)
\( \boxed{1 + 4x + 6x^2 + 4x^3 + x^4} \)
(c) Amount after one year:
Amount = \( 1000(1 + k)^4 = 1000(1 + 0.01)^4 \)
Using the expansion from (b) with \( x = 0.01 \):
\( (1.01)^4 = 1 + 4(0.01) + 6(0.01)^2 + 4(0.01)^3 + (0.01)^4 \)
\( = 1 + 0.04 + 0.0006 + 0.000004 + 0.00000001 \)
\( = 1.04060401 \)
Multiply by 1000:
\( 1000 \times 1.04060401 = 1040.60401 \)
Nearest dinar ⇒ 1041 dinar.
\( \boxed{1041} \) dinar