6. (30 points) (a) An innovative financial services company is offering a security that is like an annuity, but with payments that increase over time. Specifically, this security makes annual payments for 10 years. For A> 0 and r >0 a security can be purchased that makes a payment of B; = A(1+r) at the end of the ith year for i = 1,..., 10. For this security, we will call A the base payment and r the growth rate of the payments. Find an expression for the arbitrage free price of this security in terms of the base payment, A, the growth rate r and the discount factors d(i), i = 1,..., 10.. Show that P = 10A if and only if r is equal to the effective internal rate of return R, for the security. 2 (b) Let pi[1] denote the interest rate available at time i 1 for borrowing or investing from t = i- 1 to t= i. An investor is interested in making a swap that exchanges the sequence of payments Fx p.[1] at times i = 1, ..., 10 for a sequence of increasing payments A(1+r)' at times i = 1,..., 10. Determine the arbitrage free value for the base payment A in terms of the notional F, the growth rate r and the discount factors d(i), i = 1, ..., 10. 6. (30 points) (a) An innovative financial services company is offering a security that is like an annuity, but with payments that increase over time. Specifically, this security makes annual payments for 10 years. For A> 0 and r >0 a security can be purchased that makes a payment of B; = A(1+r) at the end of the ith year for i = 1,..., 10. For this security, we will call A the base payment and r the growth rate of the payments. Find an expression for the arbitrage free price of this security in terms of the base payment, A, the growth rate r and the discount factors d(i), i = 1,..., 10.. Show that P = 10A if and only if r is equal to the effective internal rate of return R, for the security. 2 (b) Let pi[1] denote the interest rate available at time i 1 for borrowing or investing from t = i- 1 to t= i. An investor is interested in making a swap that exchanges the sequence of payments Fx p.[1] at times i = 1, ..., 10 for a sequence of increasing payments A(1+r)' at times i = 1,..., 10. Determine the arbitrage free value for the base payment A in terms of the notional F, the growth rate r and the discount factors d(i), i = 1, ..., 10