Question

The force of interest is given by: 𝛿(𝑡) = { 0.01 + 0.01𝑡 0 ≤ 𝑡 < 4 0.15 − 0.003𝑡 2 4 ≤ 𝑡 < 6 0.06 𝑡 ≥ 6 (i) Find the expression for the value at time 𝑡 = 0 of a payment of $100 at time 𝑡.