8. Hayashi has an account that accumulates interest from time t = 0 to t = 1. Define the following symbols: A amount in account at time t = 0 B = amount in account at time t = 1 I = amount of interest earned from time t = 0 to t = 1 C = amount injected into account at time t, 0 t 1 C=C ab amount of interest earned by 1 invested from time b to time a+b, a 0, b>0,0 a+b1 Let - (1 t)i. Capital injections form an increasing annuity-immediate with twelve payments. All payments are evenly spaced with the first payment made at time tEach subsequent payment increases by an amount equal to the first payment. Show that 361 25A+11B 117' Hint: Note that B = A + C+ I with I = iA + C 1-14. Also, the following formulas may be useful n(n+1)(2n +1) 6 n(n+1) 2 [Total: 5 marks] P. 3 of 14 i=1 = = 8. Hayashi has an account that accumulates interest from time t = 0 to t = 1. Define the following symbols: A amount in account at time t = 0 B = amount in account at time t = 1 I = amount of interest earned from time t = 0 to t = 1 C = amount injected into account at time t, 0 t 1 C=C ab amount of interest earned by 1 invested from time b to time a+b, a 0, b>0,0 a+b1 Let - (1 t)i. Capital injections form an increasing annuity-immediate with twelve payments. All payments are evenly spaced with the first payment made at time tEach subsequent payment increases by an amount equal to the first payment. Show that 361 25A+11B 117' Hint: Note that B = A + C+ I with I = iA + C 1-14. Also, the following formulas may be useful n(n+1)(2n +1) 6 n(n+1) 2 [Total: 5 marks] P. 3 of 14 i=1 = =