Question

A recent college graduate has taken a new job at Work LLC, and since the company does not offer a traditional pension plan, she plans to take advantage of a tax-free investment account backed by a reputable financial institution that offers a guaranteed 8% annual return for as long as she lives.

The graduate plans on working for 45 years before retiring and will save a fixed amount each year until retirement, starting at the end of this year and continuing for all 45 years of work. Once she is retired, she expects to be able to live on the equivalent of $30,000/year in today’s terms in addition to expected social security payments. She expects annual inflation to be 4% per year over her life.

She doesn’t know how long she will live, but knows that with medical advancements, it could be for a very long time. Since one of her great fears is that she will outlive her savings, she plans to arrange retirement funding that will be in place if she were to live “forever” with the understanding that her heirs will inherit the remainder when she dies.

If she wants to save a fixed amount each year, starting with one year from now until her 45th work anniversary, how much does she need to save each year?

1. Identify the problem – All information needed to identify the problem is included in the case, and the student must select the needed information and represent it in a simplified form, which could be a combination of words and graphical representations.

2. Explain the strategy for solving the problem – Although there may be more than one way to solve a problem, the student must choose a method and explain how it will be applied.

3. Application of solution tools – The student must apply mathematical and logical tools to solve the problem. These may include formulae, logical deductions, and other appropriate devices.

4. Describe the solution – The student must provide a solution to the problem. The quality of the solution will be evaluated.

Answer 1

	1	Problem is to find the goal of savings required
		at the time of retirement and fixed amount to be saved each year
	2	Strategy:
		Calculate annual expenses required at the time of retirement
		Calculate Real Rate of Return during retirement after adjusting for inflation
		Calculate Corpus required for retirement income in perpetuity
		Calculate Fixed annual savings required during 45 years
	3	Annual expenses after retirement at current price	$30,000
		Number of years to retirement	45
		Annual inflation rate	4%
		Annual income required at the time of returement	$175,235	30000*(1.04^45)
		Nominal investment return=8%	0.08
		Inflation adjusted real return during retirement =R
		Inflation rate=4%	0.04
		(1+R)=1.08/1.04	1.038461538
		Inflation adjusted return =R=	0.038461538
		Retirement Corpus required for Perpetual retirement income	$4,556,117	(175235/0.038461538)
	Fv	Amount required at the time of retirement	$4,556,117
	Rate	Annual investment return	8%
	Nper	Number of years of fixed amount of savings	45
	PMT	Annual amount of Savings required	$11,788	(Using PMT function of excel with Rate=8%, Nper=45, Fv=-4556117)
	4	She will need to save $11,788 per year for 45 years
		At the time of retirement the total savings will be	$4,556,117
		This savings will give an inflation adjusted return of	$175,235	per year in perpetuity
		The amount of $175235 will be equivalent to	$30,000	today