Problem 1. An angel investor has the opportunity to invest in a new tech company. For an initial investment of $3, 500, 000 on 1 January, 2021, and a follow-up investment of $1, 500, 000 six months later, the investor expects that in October, 2021, she will begin to receive an annual income of $300, 000 payable quarterly in arrears for the subsequent twenty six years. However, the investor also expects that the importance of the technology to be produced will lead to competition emerging and, therefore, estimates that the annual (and hence quarterly) income will decrease by 1.1% per annum compound beginning in January, 2025. The effective rate of interest currently available to the investor is 2.3% per annum. (a) Calculate the net present value of the investment. While in discussions with the tech company, the investor is presented with the option that the annual income could instead be paid monthly. (b) Calculate, on a separate spreadsheet, the net present value of the investment if income is paid monthly. (c) On a third spreadsheet, list the respective net present values and indicate, with justification, which payment option the investor should choose. Can you also justify mathematically (in a few words) why the net present values in each case are different?

breakdown of formulas and income calulations please