3. (a) You are saving for retirement, and you can afford to save $14,400 every year, starting one year from today. If you invest for 30 years at an annual interest rate of 5.25% per year. how much will you have saved for your retirement? Hint, this is the FV of an annuity. You may want to solve parts (c) and (e), then come back and solve (b) and (d), which are annuities due. (b) How much would you have in your retirement account if you began these same 30 annual payments immediately? Hint: This is now the FV of an annuity due. c) Now let's look at things a little differently. Suppose that once you retire, you want to be able to retirement. How much would you need to have in your account when you retire to make this work jears, your acconent has zero dolliors in it. (d) How much would you need to have in your retirement account if you began these same 25 annual withdrawals immediately? Hint: This is now the PV of an anmity due Reset your calcalater to "END" of period poyments when you have finished the anmaity due problemis (e) Changing the scenario, now let's assume that you want to have $1,250,000 in your retirement account at the end of 30 years. You have now decided that you will deposif funds at the end of every month for 30 years. The interest rate is still 5.25% per year. How much do you need to deposit each month in order to reach your goal in 30 years? 4. Compare the results you got in part a) for future value of a "regular" annuity compare these to the value you got for the annuity due (part b). Now look compare the PV of the regular annuity in part (c) to the PV of an annuity due in part (d). What is the relationship that you see? Using the time value of money concepts, you have learned so far, why does this relationship (FV of regular annuity vs. annuity due and PV of regular annuity vs, annuity due) oceur? (4 points) 5. In the spring of 2022, you and your family were looking for the house of your dreams, Given your household income and your expenses, you determined that you could afford to pay $1.600 for a monthly house payment. As of April 2022, it looked like you could get a 30 -y ear mortgage rate of 3.50%. a) Given the above information, what is the maximum amount you could finance for your dream home? b) You got busy and didn't find the right home and now it is fall 2023 and you are looking at homes again. The good news is that there are more homes available for sale, but the bad news is that mortgage rates have gone up because of inflation. Assuming that you can get a rate of 7.30% APR for a 30-year mortgage and further assuming that you can still afford to pay $1,600 per month, what is the highest amount you can now finance on a home