hw-one.pdf - Anqi Lou(al44684 M339D(unique:53970 HW 1 Problem 1.1 C Problem 1.2 B Problem 1.3 D Problem 1.4 Since the force of interest is 12 the

# hw-one.pdf - Anqi Lou(al44684 M339D(unique:53970 HW 1...

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Anqi Lou (al44684) M339D (unique:53970) HW 1 01/26/2018 Problem 1.1 C Problem 1.2 B Problem 1.3 D Problem 1.4 Since the force of interest is 12%, the accumulation function is: ?(𝑡) = ? 0.12𝑡 , and since δ = 0.12 = ln(1 + 𝑟), the risk-free interest rate 𝑟 = ? 0.12 − 1 By scenario A, the present value is: 10,000 10 0 1 ?(𝑡) ?𝑡 = ∫ 10,000 10 0 × ? −0.12𝑡 ?𝑡 = 10,000 −0.12 × [? −0.12𝑡 ] 0 10 = 58,233.815 … By scenario B, the present value is: 𝑋 × ? 10| ̅̅̅̅̅ 𝑖 = 𝑋 × 1 − (1 + 𝑖) −10 𝑖 = 𝑋 × 1 − (1 + ? 0.12 − 1) −10 ? 0.12 − 1 = 5.4809 … 𝑋 Thus, 58,233.815 … = 5.4809 … 𝑋 𝑋 = \$10624.737 … Problem 1.5 At the end of the ten-year loan term, the amount of total repayment would be:

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