A. The lump sum needed at retirement is $244,360.63. B. The current assets available at retirement are $332,917.60. C. The yearly savings needed is -$88,556.97, indicating that no additional savings are required. D. The difference between needs and resources is $50,000.
To calculate the lump sum needed at retirement, we need to consider the future value of their retirement expenditures. The retirement age is 65 and they want to fund through age 92. First, we calculate the number of years they need to fund in retirement: 92 - 65 = 27 years.
Next, we calculate the future value of their retirement expenditures using the after-tax rate for investment post-retirement. We use the formula: FV = PV × (1 + r)n, where FV is the future value, PV is the present value (retirement expenditures), r is the after-tax rate for investment (5% in this case), and n is the number of years they need to fund (27 years).
Using the formula, FV = $90,000 × (1 + 0.05)²⁷ = $244,360.63.
Therefore, the lump sum needed at retirement is $244,360.63.
To calculate the current assets available at retirement, we need to consider the present value of their current savings and income. The current savings include the $110,000 they had at age 51, and the income includes their household income of $140,000, which is increasing at the rate of inflation (4%).
We calculate the future value of their household income at retirement using the formula: FV = PV × (1 + r)n, where FV is the future value, PV is the present value (household income), r is the inflation rate (4% in this case), and n is the number of years until retirement (65 - 51 = 14 years).
Using the formula, FV = $140,000 × (1 + 0.04)¹⁴ = $222,917.60.
Therefore, the current assets available at retirement are $110,000 + $222,917.60 = $332,917.60.
To calculate the yearly savings needed, we subtract the current assets available at retirement from the lump sum needed at retirement. Yearly savings needed = Lump sum needed at retirement - Current assets available at retirement = $244,360.63 - $332,917.60 = -$88,556.97. Since the result is negative, it means that the current assets available at retirement are more than enough to cover the lump sum needed, and they do not need to make any additional yearly savings.
The difference between needs and resources is the retirement expenditures minus the resources available. Difference = Retirement expenditures - (Social Security + Pension) = $90,000 - ($28,000 + $12,000) = $50,000.
--The given question is incomplete, the complete question is
"The Smiths had $110,000 in savings at age 51. They had a desired retirement age of 65. They want to fund through age 92. Assume a 4 percent inflation rate and a 5 percent after-tax rate for investment both pre- and post-retirement. They have household income of $140,000, which is increasing at the rate of inflation. Their expenditures including taxes are $125,000 a year. They estimate that in retirement they will receive $28,000 a year together in Social Security and Mr. Smith will receive a $12,000-a-year pension, both in today’s dollars. Their retirement expenditures would be $90,000 a year in today’s dollars.
1. Calculate A. The lump sum needed at retirement. B. Current assets available at retirement. C. Yearly savings needed. D. The difference between needs and resources. 2. Analysis; A. Is their retirement plan achievable as is? B. If not, what are the alternatives that could help reconcile needs and resources? C. What is your recommendation? *PLEASE SHOW CALCULATIONS."--