Ok so I have been trying to do these problems for a couple hours now, and I still can't figure them out. Please help and give as much detail in your answers as possible so I can understand it. Thank you!
Herman and Grace Rohrbach are in their mid-thirties. They are reasonably well off financially insofar as Grace's mother has established a trust fund to educate their two children. The Rohrbachs lead rather simple lives and have no desires for lavish spending. However, they do face one major financial challenge: how to have sufficient resources in their retirement years. Herman owns his own camera shop and Grace has no employment income, although she often works in Herman's store. The Rohrbachs have accumulated around $50,000 in savings, which is invested in a bond mutual fund, currently earning 5 percent after taxes. They have no other savings programs, either personal or through the business. If Herman retired today, his only income would be Social Security, which he estimates to be $18,000 annually. He would sell the business immediately prior to retirement. He has no idea what it will be worth then, but he believes he could get $100,000 for it today. To live a comfortable retirement, the Rohrbachs think they need an annual income comparable to their current one, which is $60,000 after income taxes. The Rohrbachs clearly need help to determine if they need to increase their annual savings to meet their retirement goal. Finally, the Rohrbachs will live off Social Security and interest from accumulated savings available at retirement. They will not touch any principal in their savings accounts, preferring instead to leave that money to their children. Retirement is planned in 30 years.
1. Social Security is indexed to inflation. IF the inflation rate is 3 percent over the next 30 years, how much Social Security income will the Rohrbachs receive? How much will their income (currently 60,000) be at that time, assuming it grows at the 3 percent rate? How much, then, will be the shortfall -- the difference between the two?
2. How much will be in the bond fund at retirement, assuming that it continues to earn 5 percent?
3. Herman has a very good location for his camera shop and can renew the lease indefinitely into the future. Suppose that its value increases by 10 percent annually over the next 30 years. How much will it then be worth?
4. Combine your answers to questions 2 and 3. The total represents an amount available to the Rohrbachs at the beginning of retirement. Now assume that they sell the camera shop and put the proceeds into the bond fund, and the fund continues to earn 5 percent during their retirement years. Are these annual earnings sufficiently high to meet the income shortfall determined in question 1? Your answer should be "no." Determine how much they must invest each year to accumulate a sufficient amount, which can also be deposited into a bond fund. Assume they earn 12 percent on these annual (end-of-year) investments.|||most of the questions are based on the FV of a single amount formula FV = PV * (1+i/n)^n, where PV is the present value, i is the interest rate per period, and n is number of periods
1) 18,000 * (1.03)^30 = 43,690.72 60,000 * (1.03)^30 = 145,635.70 shortfall of 101,945
2) 50,000 * (1.05)^30 = 216,097.10
3) 100,000 * (1.10)^30 = 1,744,940
4) 216,097.10 + 1,744,940 = 1,961,037 1,961,037 * .05 = 98,051.85 earnings
the last part of question 4 is a little tricky. the way i'd approach it is to determine what total amount they'd need at retirement to earn 101,945 per year (assuming it was a 5% return). once you know that amount, then subtract 216,097.10 from it. then use the FV formula to determine what annual payment invested at 12% will get you to that amount in 30 years|||No wonder you have such a problem the question is boring and it would take a lunatic to answer it.
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