Problem 2:Felix's Retirement Plan

Felix just turned 40 years-old. Although he still has many years of work ahead of him, he feels that he has not been saving enough for his retirement and wants to remediate the issue.

He makes an appointment with his banker who offers the following long-term investment scheme: Felix is to commit to invest $1,000 at the beginning of each month for the next 20 years.

These funds are to be invested 50% in bonds and 50% in stocks. The expected nominal annual return is 4% for the bonds and 8% for the stocks.

Before any penny is invested in the markets, however, the bank's management fees (5% of each $1,000monthly investment) must be paid upfront for the entire investment plan. This means that the monthly payments will first be applied to paying the bank fees for the entire amount that Felix will invest over the 20-year life of this investment plan. Once all the fees are paid, the following monthly payments willbe invested in bonds and stocks on Felix's behalf. (Note: there is no time-value-of-money calculation applied to these fees, they are just calculated as 5% of all the $1,000 monthly payments to be made by the investor throughout the 20-year life of the product).

a) What will be the $ value (to the nearest cent) of the investment in bonds at maturity, i.e., 20 years from today, after the fees are paid and assuming that the bonds perform as predicted?

b) What will be the $ value (to the nearest cent) of the investment in stocks at maturity, i.e., 20 years from today, after the fees are paid and assuming that the stocks perform as predicted?

c) What will be the true rate of return on the entire investment plan, expressed as an Effective Annual Rate (EAR), assuming that bonds and stocks perform as predicted? (the EAR should contain 4 decimals).