(a) You are given the accumulation function a(t)=(1+i)t,t0 Show that t=ln(1+i). [6 marks] (b) A fund earns interest at a force of interest t=0.05+0.01t at time t. How much interest will an initial investment of $100,000 earn between times 1 and 2 ? [8 marks] (c) In return for a promise to receive $600 at the end of 8 years, a person agrees to pay $100 at once, \$200 at the end of 5 years, and to make a further payment at the end of 10 years. Find the payment at the end of 10 years, if the nominal rate of interest is 8% convertible semiannually. [6 marks] (a) You are given the accumulation function a(t)=(1+i)t,t0 Show that t=ln(1+i). [6 marks] (b) A fund earns interest at a force of interest t=0.05+0.01t at time t. How much interest will an initial investment of $100,000 earn between times 1 and 2 ? [8 marks] (c) In return for a promise to receive $600 at the end of 8 years, a person agrees to pay $100 at once, \$200 at the end of 5 years, and to make a further payment at the end of 10 years. Find the payment at the end of 10 years, if the nominal rate of interest is 8% convertible semiannually. [6 marks]