The following case is similar to the case introduced in our third Session 1. Using general notations, the case is as follows. Consider a do-it-yourself pension fund based on regular savings invested in a bank account attracting an annual interest rate of r. Today is t=0, and you are planning to retire after n years. You want to receive a pension equal to (0,1) of your final salary and payable for the next years. In other words, the pension will be delivered between n and n+ years. Your earnings are assumed to grow at an annual rate of g, and you want the pension payments to grow at the same rate. The objective is to determine today a fraction of salary denoted by x in order to satisfy the retirement goal. 1. Provide a closed-form solution for the value of x. Note that the solution should be expressed as a function of ,r,g,n, and 2. To make sure you get the right analytical form, you need to validate your answer based on the numbers from the special case we introduced in class - see table below. Given these values, what is x? The following case is similar to the case introduced in our third Session 1. Using general notations, the case is as follows. Consider a do-it-yourself pension fund based on regular savings invested in a bank account attracting an annual interest rate of r. Today is t=0, and you are planning to retire after n years. You want to receive a pension equal to (0,1) of your final salary and payable for the next years. In other words, the pension will be delivered between n and n+ years. Your earnings are assumed to grow at an annual rate of g, and you want the pension payments to grow at the same rate. The objective is to determine today a fraction of salary denoted by x in order to satisfy the retirement goal. 1. Provide a closed-form solution for the value of x. Note that the solution should be expressed as a function of ,r,g,n, and 2. To make sure you get the right analytical form, you need to validate your answer based on the numbers from the special case we introduced in class - see table below. Given these values, what is x