Questions and Answers of Understanding The Mathematics Of Personal Finance

Today is your birthday. You are a 75 - year - old single man. You have $500,000 in the bank and $35,000 in yearly taxable income. You decided to buy an immediate fi xed annuity with a $350,000
You are a 75 - year - old woman married to a 70 - year - old man. You want to buy an immediate fi xed life annuity that will pay $2,500 a month (pretax) until the fi rst of you dies, and then$2,000 a
You have a paid - up whole life insurance policy for $250,000, listing your daughter as the sole benefi ciary. You are an 82 - year - old widower who could use some cash. Fortunately, your daughter
For most workers, the Social Security System provides a deferred life annuity. You and your employer pay into the system while you ’ re working, and then when you retire, you receive a monthly
Suppose that there never had been such a thing as a reverse mortgage and that you, an insurance company business planner, just thought of the idea. Your task now is to explain your idea by means of a
Using the calculator at the website http://www.reversemortgage.org/ , run some estimates of your own. Vary the location, the value of the home, and the age of the borrower.
Suppose that you found three stocks that are ideal examples of prices cycling up and down similar to the dollar cost averaging example above. You are convinced that these three stocks average price
The tab Sample Data in the spreadsheet Ch13Stocks.xls contains two columns of numbers that represent the prices of two stocks on 25 equally spaced (business) days. Copy these data into the stock
The company you work for has given you some option shares (calls) as a perk with a strike price of $13 a share. Sketch a graph of your profi ts and losses and indicate where you would exercise the
Repeat the above exercise assuming you had purchased these option shares at $1 a share.
Going back to the situation of problem 1, you were given calls with a strike price of $13 a share. You now sell calls with a strike price of $18 a share for $1 a share. Repeat the above, assuming
You own both puts and calls for FrisbeesAreUs, Inc. The calls have a strike price of $90 and the puts have a strike price of $85. The stock itself is selling for $88. You paid $4 for the call and $5
The coin fl ip game described in this chapter is mathematically equivalent to a “ one -dimensional random walk. ” What this means is that you fl ip the coin; if you get heads, you take a step
A state lottery offers a prize of $400 million. A single ticket ’ s probability of winning is 1/400,000,000. Assume that the state wants to make $100 million for holding the lottery and that
Evaluate the following arithmetic expressions: (a) 7 - (12-5) (b) 12(14-6) (c) 16-(3+7) 3(7-5) (d) (12-2)(7+3) (e) 12 2(7+3). (f) (12-2)7+3 (g) 6.2 + 1/3
Given that x = 6, y = 2, and z = 3, evaluate the following arithmetic expressions:2. Given that x = 6, y = 2, and z = 3, evaluate the following arithmetic expressions: (a) x + y + z (b) z(x-3)(y+2)
Refer to the table for the problem set 3:This table is for the price ( P ) of a wallet at a luggage counter over the course of a day set by a store owner who would be getting a shipment of new
Let ’ s extend problem 3 to a 2 - day rather than a 1 - day wallet sale. On the second day, the storekeeper decides to repeat his change - the - price - every - two - hours strategy, but he drops
Sketch a histogram based on the table of problem 3 using T as the horizontal axis and N as the vertical axis.
The table below shows a business plan to put items on sale. Shown are the original price and the sale price of a list of items. Calculate the percent change of all the items to the nearest percent
For x = 0.5 and then again for x = 1.2, fi ll out the table below:(Use a calculator or a spreadsheet for this problem; doing it by hand is a very tedious job.)Can you draw any conclusions about
Approximate (round) the following numbers to the nearest dollar: $12.87, $22.22, $53.50, and $1,719.88 .
The following table describes a walk I recently took. I started at 1:30 and walked until 3:30:Draw a graph using time walking (in hours) as the horizontal axis and distance walked (in miles) as the
For a simple interest loan, calculate the following:(a) The interest on a 1 - year loan of $6,700 at 10% interest per year.(b) The interest on a 3 - year loan of $500 at 6% interest per year.(c) The
The APR of a compound interest loan = 18.0%. What is the compounding rate if the interest is compounded once, twice, three times, or four times a year?
A loan with an APR of 7.5% is compounded annually. If $1,250.00 is borrowed, fi nd the balance each year for 3 years.
I took a loan for $10,000 that is accruing interest at an APR of 7.5%, compounded monthly.What is the balance every month for 18 months?
For the same loan as above, I decide to pay the loan back 13 days after my eleventh payment, in a 28 - day month. What is my balance on the payoff day?
For the loan of problem 4, assume that my lender wanted an up - front fee of $250 to set up the loan. I want the lender to fold this fee into the loan. First, repeat problem 4 showing this up - front
For the calculations in this problem, assume that the interest is compounded annually.Suppose you are able to take a 10 - year loan at the loan rates shown in the table , and you are able to save the
Find the regular monthly payments for the following loans (that accrue interest monthly):(a) Principal = $100,000; rate = 6.00%; 15 years(b) Principal = $230,000; rate = 9.10%; 20 years(c) Principal
Using the loan from problem 1a above, assume that the loan originated in July of 2005 and that the interest is deductible from your taxes. How much interest did you pay in the calendar years 2005,
Using the loan from problem 2 above , after which payment (payment number, month, and year) did you pay off more than half of the principal?
Again using the loan from problem 2, in May of 2013, instead of your regular payment, you send in $10,000.00. Assuming that your lender is agreeable to recalculating, what will your regular payments
Again using the loan from problem 2 , but start the loan in January for convenience, you have a job that pays you a small subsistence salary monthly and then sends you your commission checks
You have decided that you can make $1,000 a month payments on a 20 - year loan. Calculate and plot a graph of the amount you can borrow versus the interest rate you can get, for interest rates
You are buying a new car for $31,800.00. You have $5,000 for a down payment and you wish to fi nance the remainder over 4 years. The car dealer offers you a 7% loan with up -front costs of $250. You
Your up - front costs for getting your loan were 3 points and $450.00 in fees. You didn ’ t have this money available, so you had these costs folded into the loan. What ’ s your effective
Since you are short on cash, you make interest - only payments on the above loan for the fi rst 3 years. How much are these payments, what is your balance at the end of 3 years, and what is your new
Continuing with the above situation, after 5 years (Pmt Nr 60), interest rates drop and you are offered a free refi nancing of the loan at 5.00%. You ’ d like to pull some cash out for other
I bought a house that was appraised at $425,000 on January 1, 2000. I got an 80% mortgage as a fi xed 30 - year mortgage at 5.00%. On January 1, 2007, I decided to take a second mortgage because I
Consider a $25,000, 5 - year auto loan with a fi xed interest rate of 7.6%.(a) After which monthly payment does the worst case rule of 78 prepayment penalty occur and how much is this penalty?(b) If
Assume that you have a savings account that pays 7.00% annual percentage rate (APR), compounded monthly, with $100,000 in it on the day you bought your car. The best money -managing philosophy would
Repeat the same problem but with a savings interest rate of 8.0%.
Assume a purchase interest rate of 0.0333% per day. The current month has 30 days, and the billing period is from day 1 to day 30. You have no previous balances.(a) You charge a $150 purchase on the
You are always a little short of cash before your payday, which is the last day of each month. The last day of your credit card billing period is also the last day of each month.On the twentieth day
Assume a purchase daily interest rate of 0.03% and a cash advance interest rate of 0.06%.You make a purchase of $150 on the fi rst day of the month and take a cash advance of$250 on the twentieth day
I take a $22,000 auto loan, payable monthly at 6.00% APR for 5 years (60 payments). If I can save money at 4.00%, what is the present value of this loan the day that I take it?
A TV store dealer will “ let me have ” a $2,300 TV for 24 monthly payments of $100.00, the fi rst payment due on the day I take the TV out of his or her store. Under what circumstances is this a
Consider a fi xed rate, fi xed payment 15 - year mortgage loan for $350,000. I ’ ll consider the present value of the loan when I take the loan to be my actual cost of the loan. If I want to keep
Find the monthly payments for the above situation, using APRs of 0%, 2%, 4%, 6%, 8%, and 10%. Then divide each monthly principal by its accompanying payment, giving you the ratio of principal :
In this chapter, I argued that the best choice for a loan is the loan with the lowest present value, subject to the constraint that you have to be able to afford the payments. We could consider a fi
You have a 15 - year, $350,000 mortgage with a 5.00% APR. Eight years into the mortgage, you get the opportunity to refi nance with a new 8 - year loan for the remaining balance of your loan at 4.2%.
I want to buy a new home and I need to borrow $500,000. Lender A has a very attractive APR of 5.10% on a fi xed 30 - year mortgage, but he or she will only lend me $350,000.Lender B will give me a
Suppose that you and your signifi cant other each have a taxable income of $50,000 a year.The two of you could fi le your taxes as each being single, as being married fi ling jointly, or as being
Consider the same problem as above, but in this case, one of you has a taxable income of$10,000 while the other has a taxable income of $90,000.
This problem continues the study of Chapter 8 , Comparing Loans. You have the choice of two competing mortgage loans, both for $350,000. You can get a 6% APR 15 - year loan or a 6.5% APR 20 - year
When you retire, you want to spend $40,000 a year from your savings to help support yourself. Infl ation is running at 3% a year, however, and you notice that it costs you a little more each year to
You are (one of) a married couple fi ling jointly. Your taxable income this year will be about $100,000. You have about $25,000 to save or invest. Infl ation is running at 2.5%annually. What APRs
A - 50 - year old man decides that he wants a $1,000,000 life insurance for 2 years.(a) What will two separate 1 - year term policies cost, both bought at the beginning of the fi rst year? Use 4%
Suppose someone was to come down with an incurable terminal disease and was told by his or her doctor that “ You have a two - third chance of lasting a year; you ’ ll never last more than 2
Using the half year Life Table shown in Table 10.6 , assuming an APR of 4% for the present value, what is the cost (idealized) of an 18 - month, $50,000 term policy for a man starting halfway through
Life Tables can be generated for longer time steps than 1 year as well as for shorter time steps than 1 year. Tables generated in 5 - year steps are sometimes called abridged Life Tables. Starting
You are taking a 5 - year business loan for $250,000 that you will amortize yearly with 60 equal monthly payments at an APR of 10%. Your lender wants a fully paid - up life insurance policy to