1)

Sofi wants to make withdrawals of $38,734 at the end of each year for 5 years to pay for college. Her first withdrawal occurring in 11 years. She plans to finance these withdrawals with 3 savings payments of $25,826 in 2 year from today, $X 4 years from today and $15,524 8 years from today. How much must she deposit 4 years from today (X) to meet her goal if she can borrow and lend at 3.18% interest per year compounded annually.

Hint: this is a 2 part problem, the present value of the annuity, what she plans to spend will define how much she needs to save. From there you can backout X.

2)

Spence wants to have $441,308 in 10 years. He plans to make regular savings contributions of $2,934 at the end of each quarter for 10 years, with the first of these regular savings contributions made in one quarter. He also expects to make a special savings contribution of X in 10 years. He expects to earn 8.37% per year on his savings. What is X, the amount of the special savings contribution that Spence will make in 10 years?

3)

Howard plans to make regular savings contributions of $19,279 per semiannual period for 25 years with his first regular savings contribution one semiannual period from today. Suppose he also plans to make a one-time contribution of $18,651 in 12 years from today. How much would Howard expect to have in his account 25 years from today if he earns 6.81% on his savings?