Question

Your financial planner offers you two different investment plans. Plan X is a $25,000 annual perpetuity. Plan Y is a 15-year, $35,000 annual annuity. Both plans will make their first payment one year from today. At what discount rate would you be indifferent between these two plans? Your friend is celebrating her 35th birthday today and wants to start saving for her anticipated retirement at age 65. She wants to be able to withdraw $125,000 from her savings account on each birthday for 20 years following her retirement; the first withdrawal will be on her 66th birthday. Your friend intends to invest her money in the local credit union, which offers 7 percent interest per year. She wants to make equal annual payments on each birthday into the account established at the credit union for her retirement fund.

a. If she stents making these deposits on her 36th birthday and continues to make deposits until she is 65 (the last deposit will be on her 65th birthday), what amount must she deposit annually to be able to make the desired withdrawals at retirement?
b. Suppose your friend has just inherited a large sum of money. Rather than making equal annual payments, she has decided to make one lump sum payment on her 35th birthday to cover her retirement needs. What amount does she have to deposit?
c. Suppose your friend's employer will contribute $3,500 to the account every year as part of the company's profit-sharing plan. In addition, your friend expects a $175,000 distribution from a family trust fund on her 55th birthday, which she will also put into the retirement account. What amount must she deposit annually now to be able to make the desired withdrawals at retirement?

Answer 1

This question involves comparing investment plans and determining deposit amounts for retirement savings. It requires the present value and future value formulas for annuities and uses a 7% interest rate. Adjustments are made for additional employer contributions and trust fund distributions to find the necessary annual deposits.

Step-by-step explanation:

The question involves the comparison of two investment plans, and calculating the required yearly deposits and lump sum payment needed for a retirement account. To evaluate the indifference point between Plan X and Plan Y, we would use the formula for the present value of a perpetuity and an annuity, considering that both start one year from today. For the retirement account scenarios, we apply the formula for the present value of an annuity and future value of an annuity to determine the amounts needed.

For the part of the question involving the retirement savings plan, we need to find the present value of an annuity of $125,000 for 20 years, with a 7% annual interest rate, to determine the lump sum payment. When considering annual payments, the question becomes a matter of finding the equal annual deposits that would result in the desired future value at retirement.

When an additional employer contribution and a one-time trust fund distribution are introduced, we adjust the required annual deposits by first finding the future value of these added funds at the moment of retirement and then calculating the adjusted annual deposits needed.