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Mr. Smith has saved $1,800 each year for 20 years. A year after the saving period ended, Mr. Smith withdrew $7,500 each year for a period of 5 years. In the sixth and seventh years, he only withdrew $5,000 per year. In the eighth year, he decided to withdraw the remaining money in his account. If the interest rate was 6% per year throughout the whole period, what was the amount he withdrew at the end of the eighth year?

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Darryn D'Souza
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28 Sep 2019

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Related questions

John and Peter both want to save some money. John decides to save $1,000 every year in an account that pays 4% interest per year compounded annually. Peter is a little less organized and doesn’t get around to depositing money into his savings account, which also pays 4% interest per year compounded annually, until 5 years later. He thinks he’ll try and make up the time by depositing $1,400 into the account every year from then on. How much will be in each person’s account at the end of 20 years, counting from when John started saving, compared to the total amount that each person put in?

After analyzing their social securities statements, Charles and Susan are not so sure that their social security benefits will be enough to cover their estimated monthly expenses if they are planning to retire at age 66.
The Smiths are considering opening an IRA account in 2016, after researching the pros and cons of each retirement account; they decided that Roth IRA will fit with their retirement goals. Based on the current IRS regulations, the limit for annual contributions for “Married filling jointly” and Income limit of $183,000 or less is $5,500 for 2016, and $6,500 for people over 50.

Questions:

1. Calculate the total future worth of their Roth IRA account right on their 65th birthday (Normal retirement age) if Charles and Susan will deposit the maximum contribution amount allowed by IRS of $5,500 every year starting at the end of 2016 (age 40) and for the next 9 years (age 49), and then they are planning to increase their contribution to $6,500 for the next ten years (starting age 50) until they are both 65 years old. Assume the couple will not withdraw any money from their IRA during the next 25 years and the Roth IRA account will earn a) 4% and b) 6% per year.

2. The Smith’s forecasted their retirement expenses to be $24,000 starting one year after their retirement age (65 years old). Ignoring any Social Security Benefit. In other words, assuming their $24,000 annual expenses will be funded only with distributions from their Roth IRA (Future worth calculated on question 1). How long will they be able to withdraw $24,000 before exhausting all their IRA funds, assuming a Roth IRA account will earn in average account will earn a) 4% and b) 6% per year?

3. What is the maximum amount of money they can withdraw every year out of the Roth IRA account in order to deplete all the funds by their 85th birthday (use n=20 years in your calculations) Assuming a Roth IRA account will earn in average a) 4% and b)6% per year?

Alternatives and Costs

In the fall, Jay Thompson decided to live in a university dormitory. He signed a dorm contract under which he was obligated to pay the room rent for the full college year. One clause stated that if he moved out during the year, he could sell his dorm contract to another student who would move into the dormitory as his replacement. The dorm cost was $5,000 for the two semesters, which Jay had already paid.

A month after he moved into the dorm, he decided he would prefer to live in an apartment. That week, after some searching for a replacement to fulfill his dorm contract, Jay had two offers. One student offered to move in immediately and to pay Jay $300 per month for the eight remaining months of the school year. A second student offered to move in the second semester and pay $2,500 to Jay.

Jay estimates his food cost per month is $500 if he lives in the dorm and $450 if he lives in an apartment with three other students. His share of the apartment rent and utilities will be $400 per month. Assume each semester is 4.5 months long. Disregard the small differences in the timing of the disbursements or receipts.

(a) What are the three alternatives available to Jay?

(b) Evaluate the cost for each of the alternatives.

(c) What do you recommend that Jay do?

From Chapter 2

Fixed, Variable, Average, and Marginal Costs

One of your firm’s suppliers discounts prices for larger quantities. The first 1,000 parts are $13 each. The next 2,000 are $12 each. All parts in excess of 3,000 are $11 each. What are the average cost and marginal cost per part for the following quantities?

(a) 500

(b) 1,500

(c) 2,500

(d) 3,500

Fixed, Variable, Average, and Marginal Costs

A new machine comes with 100 free service hours over the first year. Additional time costs $75 per hour. What are the average and marginal costs per hour for the following quantities?

(a) 75

(b) 125

(c) 250

Segmenting Models

SungSam Inc. is designing a new digital camcorder that is projected to have the following per unit costs to manufacture:

Cost Categories Unit Costs

Materials costs $63

Labor costs 24

Overhead costs 110

------

Total unit cost $197

Sungsam adds 30% to its manufacturing cost for corporate profit.

(a) What unit profit would Sungsam realize on each camcorder?

(b) What is the overall cost to produce a batch of 10,000 camcorders?

(c) What would Sungsam’s profit be on the batch of 10,000 if historical data show that 1% of product will be scrapped in manufacturing, 3% of finished products will go unsold, and 2% of sold product will be returned for refund?

(d) How much can Sungsam afford to pay for a contract that would lock in a 50% reduction in the unit material cost previously given? If Sungsam does sign the contract, the sales price will not change.

Cash Flow Diagrams

Pine Village needs some additional recreation fields. Construction will cost $225,000 and annual O&M expenses are $85,000. The city council estimates that the value of added youth leagues is about $190,000 annually. In year 6 another $75,000 will be needed to refurbish the fields. The salvage value is estimated to be $100,000 after 10 years. Draw the cash flow diagram.

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