Pembahasan Ujian PAI: A10 – No. 27 – April 2024

$$\text{Convexity} = \frac{\sum_{t=1}^{n} t \times (t+1) \times C_{t}\,v^{t+2}}{\sum_{t=1}^{n} C_{t}\,v^{t}}$$

$$\text{Convexity} = \frac{1 \times 2 \times 1v^{3} + 2 \times 3 \times 3v^{4} + 3 \times 4 \times 7v^{5}}{1v + 3v^{2} + 7v^{3}}$$
$$\text{Convexity} = \frac{1 \times 2 \times 1(1{,}1)^{-3} + 2 \times 3 \times 3(1{,}1)^{-4} + 3 \times 4 \times 7(1{,}1)^{-5}}{1(1{,}1)^{-1} + 3(1{,}1)^{-2} + 7(1{,}1)^{-3}}$$
$$\text{Convexity} = \frac{65{,}95426}{8{,}64763}$$
$$\text{Convexity} = 7{,}62686 \approx 7{,}63$$

Dengan demikian, diperoleh nilai konveksitas pembayaran tersebut sebesar 7,63.