(Solve manually) Lucy, has just turned 27 years old today and wants to retire at age 63. When she retires she wants to have enough money to purchase a 27-year annuity that will pay $4.000 per month. Monthly payments should start on her birthday when she reaches age 63 years old. The annuity earns 3.25% rate of return (compounded annually).

To achieve her financial goals, Lucy needs to invest $X every month. She has identified 2 types of investments she weill invest her money into:

option 1:

a portfolio of technology stocks managed by Lucy's bank. this portfolio offers an annual rate of return of 7.50% (compounded annually).

option 2:

A mutual fund comprising of fixed-income instruments. This fund offers and annual rate of return of 4.25% (compounded semi-annually).

Lucy will put 50% of $X into option 1) and 50% of $X into opotion 2). How much will she have to save each month (I.e solve for $X) starting one month from now to age 63 for her to reach her retirement goal?