Task: Assume that at time 0 a sum L is lent for a series of n yearly payments. The rth payment, of amount Xr, is due at the end of the rth year. Let the effective annual interest rate for the rth year be ir Give an identity which expresses L in terms of the X, and ir. Answer: The identity is [ Select ] [Select] L = x_1 (1+i_1)^(-1) + x_2 (1+i_1)^(-1) (1+i_2)^(-2) + ... + x_n (1+i_1)^(-1) (1+i_2)^(-2) ... (1+i_n)^(-n) L = x_1 (1+i_1) +x_2 (1+i_1) (1+i_2) + ... +x_n (1+i_1) (1+i_2) ... (1+i_n) L = x_1 (1+i_1)^(-1) + x_2 (1+i_1)^(-1) (1+i_2)^(-1) + ... + x_n (1+i_1)^(-1) (1+i_2)^(-1) ... (1+i_n)^(-1) L = x_1 (1+i_1) +x_2 (1+i_1) (1+i_2)^2 + ... +x_n (1+i_1) (1+i_2)^2 ... (1+i_n)^n