Bowie, age 52, has come to you for help in planning his retirement. He

Bowie, age 52, has come to you for help in planning his retirement. He works for a bank, where he earns $60,000. Bowie would like to retire at age 62. He has consistently earned 8% on his investments and inflation has averaged 3%. Assuming he is expected to live until age 95 and he has a wage replacement ratio of 80%, how much will Bowie need to have accumulated as of the day he retires to adequately provide for his retirement lifestyle?

2 months ago

Solution 1

Guest Guest #2390893
2 months ago


Bowie will require  saving for $1,101,832.05 to achieve their goal.


He expect to have wages 800% of what he currently owns:

60,000 x 80% = 48,000

Now, this will increase 3% per year for inflation reasons:

Principal \: (1+ r)^{time} = Amount

Principal 48,000.00

time 10.00

rate 0.03000

48000 \: (1+ 0.03)^{10} = Amount

Amount 64,507.99

Now, we solve for the present value of an annuity of 33 year (95 - 62) with a real rate according to Irwin method of:

\frac{1+r_n}{1+\theta } -1 = r_r

1.08/1.03 - 1 = 0.048543

C \times \frac{1-(1+r)^{-time} }{rate} = PV\\

C 64,507.99

time 33

rate 0.048543

64507.99 \times \frac{1-(1+0.048543)^{-33} }{0.048543} = PV\\

PV $1,101,832.0536

📚 Related Questions

J P] Corp has sales of $6 million, accounts receivable of $950,000, total assets of$25 million ( of which $18 million are fixed assets), inventory of $860,000, andcost of goods sold of $2,200,000. What is J P] ’5 accounts receivable days? Fixedasset turnover? Total asset turnover? Inventory turnover?
Solution 1


The accounts receivable days: 57.79 days

Fixed asset turnover: 0.33 times

Total Asset Turnover: 0.24 times

Inventory turnover: 2.56 times


The accounts receivable days is calculated by the formula:

The accounts receivable days = (Accounts receivable/Annual Sales) x 365 = ($950,000/$6,000,000) x 365 = 57.79 days

Fixed asset turnover = Net Sales/Fixed assets = $6,000,000/$18,000,000 = 0.33 times

Asset turnover helps investors understand how effectively companies are using their assets to generate sales. Asset turnover is calculated by using following formula:

Total Asset Turnover =  Total Sales/Total Assets  = $6,000,000/$25,000,000 = 0.24 times

Inventory turnover = Cost of Goods Sold/Inventory = $2,200,000/$860,000 = 2.56 times

Suppose that Lucy’s demand for private concerts (performed by Schroeder) is given by the following equation Suppose that the cost of concerts is $2. What is Lucy’s Consumer Surplus? a. 15 b. 10 c. 12.50 d. 20
Solution 1


d. 20

Missing Information:

Qd = 15 - \frac{5}{2} P


TO sovle for the consumer surplus we need to get the equilibrium price and quantity.

If P = 2 then:

Qd = 15 - (5 / 2) x 2 = 15 - 5 = 10

Now we need to knwo how much is the price that makes Lucy do not consume:

We solve for Qd = 0

0 = 15 - (5/2) x P

p = 15 / (5/2) = 6

Now we calculate the area of the consumer surplus which is the area of the demand curve above the equilibrium price.

10 x (6-2) / 2 = 10 x 4 / 2 = 20

Employment tends to a. lag the cycle. b. lead the cycle. c. be coincident with the cycle. d. sometimes lead, sometimes lag the cycle.
Solution 1


A) lag the cycle.


One of the basic mistakes made by classical economists is that they believe that wages and employment are economic variables that can be easily controlled like money supply or interest rates, when actually they are extremely inflexible and they usually vary much less than the economic cycle.

For example, no employee will accept a pay cut, it is easier for the company to fire him than to convince him/her o earn less money. This is logical since I wouldn't accept a pay cut and you probably wouldn't either. Employment as a whole is more closely related (but in the opposite direction) to the inflation rate than to the economic cycle.

Even the government (at all 3 different levels) tries to avoid massive layoffs since a person fired is not simply a lower cost, but it has negative impacts on the economy as a whole and at social and community levels also.

You must also remember that it sometimes is much easier to fire someone than to hire him/her again or someone with similar skills to perform a job once the economy rebounds.

Solution 2


The correct answer is letter "A": lag the cycle.


Business Cycle Indicators (BCI) are variables pooled in an index that helps to measure the health of an economy. The main variables included considered BCI are production and employment. Usually, economic cycles are characterized by an increase in production and employment and after reaching its highest peak comes to a decline heading towards the economy's lowest point.  

Employment tends to lag the cycle because it measures how the economy performed. It cannot lead the cycle since employment does not predict future events.

4. The Mexican peso has weakened considerably relative to the dollar, and you are trying to decide whether this is a good time to invest in Mexico. Suppose the current exchange rate of the Mexican peso relative to the U.S. dollar is MXN 9.5/USD. Your investment advisor at Goldman Sachs argues that the peso will lose 15% of its value relative to the dollar over the next year. What is Goldman Sachs’s forecast of the exchange rate in 1 year?
Solution 1


The forecast exchange rate in one's year time according to Goldman Sachs is MXN 14.25/USD


The fact that the Mexican Peso will lose 15% of its value to the dollar means that a dollar will command 15% of the current Peso value  in  a year's time.

Mathematically, MXN 9.5*1.15= MXN14.25 in a year's time.

It also implies that a Mexican with dollars wanting to convert into MXN in a year's time will receive more Peso compared to now.

4. What would you expect to happen to the spread between yields on commercial paper ant Treasury bills if the economy were to enter a steep recession?
Solution 1

Answer: I will expect the spread between the yields to WIDEN

Explanation: The spread between the yield on Treasury bills and commercial paper will widen if the economy were to enter a steep economy.

A downward slope in the economy increases credit risk. It leads to a situation whereby Investors demand a greater premium on debt securities which are subject to default risk.

A company reports the following: Sales $3,150,000 Average accounts receivable (net) 210,000 Determine: (a) the accounts receivable turnover and (b) the number of days' sales in receivables. Round interim calculations to the nearest dollar and final answers to one decimal place. Assume a 365-day year.
Solution 1


a. 15 times

b. 24.3 days


The computation is shown below:

a. Accounts receivable turnover

Account receivable turnover ratio = Net credit sales ÷ Average accounts receivable  

= $3,150,000 ÷ $210,000

= 15 times

b. Number of days sales in receivables = Total number of days in a year ÷ accounts receivable turnover ratio

= 365 days ÷ 15 times

= 24.3 days

Which of the following best describes an intermediate error event? Multiple Choice It is a boundary event attached to the boundary of an activity. It indicates alternate sequence flow begins when an error occurs. O It is modeled with a leaning Z or flash sign. o All of the choices describe intermediate error events. None of the choices describe intermediate error events.
Solution 1

Answer:All of the choices describe intermediate error events.

Explanation:Intermediate error events are triggered when a token causes a fault name to be raised in a normal flow, going through to an Error End Event. Intermediate error event shows changes in the normal sequence caused by an exception in the process. There are basically 2ways in which intermediate error event can be used, it includes when used as a sequence flow of a process or as boundary events related to certain activity or activities, it indicates alternative sequence flow,it is noted with a leaning flash or z sign.

A company intends to install new management software for its warehouse. The software will cost $ 55, 000 to buy and will cost an additional $ 151, 000 to install and implement. It is anticipated that it will save the company $ 39, 000 through reductions in staff and $ 63, 000 in general inventory costs in the first year after installation. a. What is the benefit to the company in the first year if they choose to install the​ software?
Solution 1


By choosing to install the software the company will lose $104,000 as the costs of installation far outweigh the benefits derivable from deploying the new management software.


Find below detailed calculation of the benefits or(loss) from this course of action:

The loss =Total benefits-total costs

The cost of software         $55,000  

Cost of installation          $151,000  

Total cost of software          $206,000  



Reduction in staff                   $39,000  

Saved general inventory costs      $63,000  

Total benefits                            $102,000  

Loss from implementing software ($104,000)

The software's deployment would have been worthwhile if the benefits is for a long term,hence the costs can be spread over a number of years.

Your monthly spreadsheets confirm what you had suspected: neither New York nor Chicago is big enough for both you and your competition. Chicagoans clearly prefer the rich heartiness of your deep-dish pizza, whereas New Yorkers go for the light, flaky crust of your chief rival. In time, you feel that the battle for New York could be won, but you are pretty sure the competition feels the same way about Chicago. You can save transportation and assorted costs by pulling out of New York completely and concentrating on the Windy City, but you don't want to give up a marginally profitable operation in the Big Apple unless you get some concessions. Should you.. A) Expand your Chicago operations and gradually withdraw from New York
Solution 1

Answer:it is advisable for the firm to expand their Chicago operations and gradually withdraw from New York.


The market share is the percentage of the market sales that a firm control than their competitors in the market. When a firm wants to expand their operations to new market, it means they want to compete for a share of the market with other firm in the market. What they have to do in order to succeed is that, they have to put in place new strategies that will enable them to take control of the market away from their competitors.

In a perfectly competitive market, profit is maximized when MC = MR, marginal profit can be used to either expand or reduce business operations. In the sense that, a firm should put a stop to their desire for expansion when the marginal cost is reducing profit. As a business is expanding it's cost structure will also experienced an increase. Therefore, in this case transportation cost and assorted cost is a marginal cost which they can save by pulling out of New York completely and concentrating on the Chicago city operation . It is however advisable for the firm to expand Chicago operations where Chicagoans prefer their product than the product of their competitors and gradually withdraw from New York where their competitors have a larger share of the market than them.

You just won the lottery. Congratulations! The jackpot is $35,000,000, paid in six equal annual payments. The first payment on the lottery jackpot will be made today. In present value terms, you really won —assuming annual interest rate of 9.50%.
Solution 1




The annual amount that I would receive = $35,000,000 / 6 = $5,833,333

There are 6 annual payments that I will receive, one of them is to be received today so its should not be discounted as $1 today is worth $1 today but after a passage of time would not be $1, it might be worth $0.9.


Present Value =   Cash flow  *  1 / (1+r)^n

Remember that r is the discount rate  and n is the number of years.

Y0 PV =  $5,833,333  

Y1 PV =   $5,833,333 * 1/(1+9.5%)^1 = $5327245

Y2 PV =  $5,833,333 * 1/(1+9.5%)^2 = $4865064

Y3 PV =  $5,833,333 * 1/(1+9.5%)^3 = $4442981

Y4 PV =  $5,833,333 * 1/(1+9.5%)^4 = $4057517

Y5 PV =  $5,833,333 * 1/(1+9.5%)^5 = $3705495

Y6 PV =  $5,833,333 * 1/(1+9.5%)^6 = $3384013

Present Value of Lottery = (Y0 PV + Y1 PV + Y2 PV + Y3 PV + Y4 PV +Y5 PV + Y6 PV)

Present Value of Lottery = $5,833,333 + $5327245 + $4865064 + $4442981 + $4057517 + $3705495 + $3384013 = $31615648

So this is the amount that I will receive in todays value.