You want to save money to meet two goals. First, you are cu…

Questions

Yоu wаnt tо sаve mоney to meet two goаls. First, you are currently 25 years old and aim to retire in 40 years (at the age of 65), with a plan to secure a retirement income of $100,000 annually for 25 years (i.e., withdrawals from your retirement account). You will make your first withdrawal 41 years from now, and your final withdrawal will occur 65 years from today, when you are 90 years old. Second, you plan to travel to Europe 45 years from now, which is five years after your retirement. For this trip, you will need an additional $30,000 that year, in addition to the regular $100,000 retirement income. Two years before retiring (38 years from now), you plan to relocate to your vacation home and sell your primary residence, which you anticipate selling for $110,000. The proceeds from this sale will be deposited into your retirement account and used to cover your retirement expenses. (25 points) If you can earn a 12% Effective Annual Rate (EAR) in your retirement account, which corresponds to a 12% Annual Percentage Rate (APR) compounded annually (m=1), how much would you need to save annually over the next 40 years? Assume your first savings contribution starts one year from now, and your final contribution will be in the 40th year, with the contribution amount being the same each year. (5 points) Now, suppose you opt for quarterly contributions to achieve your retirement goals, starting with your first savings installment one quarter from today. You plan to save an equal amount every quarter. To meet your goals, how much do you need to save each quarter over the next 40 years? Your final contribution will be made at the end of the 40th year, which corresponds to 160 quarters from now. Assume you can earn 12% EAR (which corresponds to a 12% APR compounded annually) in your retirement account. Show your work.