A Bunch of Present Value, Future Value, etc. problems compiled, over the years, by

Professor Christopher Spivey, Ph.D., Professor Emeritus of Finance, The Citadel

 

  1. A leading newspaper incorrectly reported a 12% annual rate of inflation based on a recent 1% monthly increase in the consumer price index.  What is the correct annual rate of increase?  (Hint:  there are 12 periods in this problem)

 

  1. You own a five-gallon gas can that happens to be full of gas.  Two motorists run out of gas in front of your home; the first offers to pay you $25 now in exchange for the gas, and the second bids $35 paid 5 years from now with his mint-condition spare tire held as security.  If the money would be kept in your 5% savings account, which offer would you accept?

 

  1. If your rich uncle holds your IOU for $5000 due in 3 years, what would you be willing to offer him now if you wanted to redeem it?  If you do not redeem it, you plan to purchase a 3-year certificate of deposit yielding 7 ¾%.

 

  1. It so happens that you are anxiously awaiting the design, manufacture, and marketing of a fuel-less, wind-powered automobile that is expected to be completed in four years.  It has a set delivery price of $10,000, but in order to assure delivery money must be deposited today in a non-interest-paying escrow account that charges a 4% annual service fee.  Since the escrow account must have $10,000 in four years, how much must you put in the account today?

 

  1. In July of 1978, you paid $95 for a 10-ounce silver ingot issued by the Benjamin Mint commemorating the July, 1969 Apollo 11 landing.  The collector who sold it to you bought it when it was issued and told you that he realized a 2% annual rate of loss on this investment.  What did he pay for the ingot? [NB: Assume the ingot was issued in July 1968, at the time of the landing]

 

  1. In 1626 Manhattan Island was purchased from the Indians for a mere $24 worth of trinkets.  Three hundred and fifty years later the island, less improvements, had a value of fifteen billion dollars ($15,000,000,000.)  If the Dutch settlers instead had the option of depositing the $24 in a 6% account in the Bank of Amsterdam, and if their heirs had moved the deposit to the Bank of England in 1819 when the Amsterdam bank wound up its affairs, who got the best of the deal, the Indians or the settlers? [NB: Assume BOE also paid 6% p.a.]

 

  1. The Euphorian tribe of the Euthanasian Islands sets aside a fund at birth to finance the newborn’s eventual funeral and ceremonial expenses.  According to tradition, a first class ceremony (for a chief or heir apparent only) costs 30,000 cowrie shells and the life expectancy for male members of the royal family is 70 years.  How many cowrie shells should be deposited with the tribal treasurer (who at the end of each year pays in one cowrie shell for each ten on deposit) to fully fund the funeral expenses of the Chief’s first son, born this year?

 

  1. The Last National Bank in your hometown is trying to attract additional deposits by compounding and paying interest daily.  You have a modest $100 deposit in another bank which pays the same interest (5% on regular passbook accounts), but compounds the interest quarterly.  How much larger would your account be at the end of one year if you switched banks in order to take advantage of the daily compounding?  (Hint:  set your calculator for floating decimal and use a 360-day year)

 

  1. Six months ago you got a $1000 birthday bonus which you immediately put to use as a stake in your scheme to make an immodest fortune in the commodities market.  The $1000 was deposited with your broker as security on your contract to sell 5000 bushels of number 1 Canadian rapeseed at $3.10 per bushel for delivery in Thunder Bay, Ontario the following December (today).  Not only have you never owned the 5000 bushels that you have contracted to sell, but you would not know a rapeseed if you were accosted by one.  If rapeseed sells for $3.22 per bushel in December (when your contract calls for deliver), what monthly discounted rate of return did you get on your investment?

 

  1. In 1975, a prominent local bank offered an “instant interest” certificate of deposit in attempt to evade Regulation Q limits on maximum rates of interest paid on small certificates.  All interest that would accrue during the life of the certificate was paid at the time it was purchased, hence the term “instant interest.” The highest rate available was 7 ½% and the longest maturity was 6 years.  Since the instant interest provision in effect lowers the purchase cost of the CD, what would be the rate of return on your investment if you bought one of these 7 ½% CDs?

 

  1. Suppose that you have $275 today and you make a deposit in an account that compounds the interest annually.  If you close the account and withdraw $556.12 in exactly 16 years, what interest rate was paid to you during that period?

 

  1. If your great-granddaddy opened a $500 savings account on your behalf when you were born, and if you just found out that the amount had a value of $1621.70, how old are you if the deposit has been compounding at a 4% annual rate?

 

  1. The last time we looked, our colony of Bacillus megaterium was still growing like a weed.  If the colony had 18,114 cells before lunch and is still growing at a rate of 2% a minute, how long a lunch break did we take if we found a colony of 107,652 when we got back?  (Hint:  the tables don’t have enough periods.)

 

  1. Assume that you are twenty years old, a senior in college, and are considering an M.B.A. program that takes one year to complete.  You also have been told that someone who holds an M.B.A. earns about $3000 per year more than someone who holds a B.S.  Using a discount rate of 8 ½%, what is the present value of the extra income you would receive over the course of your lifetime if you decided to get the M.B.A. and retire at age 65?

 

  1. At the time of this writing, a popular national magazine subscription was $8.50 per year or $200 for a lifetime membership if the subscriber is age 10 or older.  Would it be cheaper for you, a white male age 20, to subscribe on an annual basis or pay the lifetime subscription rate?  If you didn’t buy the lifetime subscription, you could invest your $200 elsewhere and get a 7 ½% return.  (Now we’ve got an annuity due; the first payment is due at the start of the first time period, before any of the issues are received.)  A life expectancy table tells us that the average 20-year old white male has 50.1 years left.

 

  1. If you lived forever, what would be the present value of an $8.50 perpetual annuity discounted at 5%?

 

  1. In June, 1976 the South Carolina Watermelon Growers’ Association awarded a talented bystander $50 for spitting a watermelon seed 25 feet and 7 inches, a feat that won first prize in a contest they sponsored.  If our bystander puts the prize in a special 5% Fourth of July Watermelon Fund to purchase watermelons for an Independence Day party each year for the next 16 years, how much can he spend on each year and have nothing left after the 16th party?  (The interest in the fund is compounded annually.)