Amortized loans More on the time value of money is a divorce attorney who practi

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Amortized loans

More on the time value of money is a divorce attorney who practices law in Florida. He wants to join the American Divorce Lawyers Association (ADLA), a professional organization for divorce attorneys. The membership dues for the ADLA are $550 per year and must be paid at the beginning of each year. For instance, membership dues for the first year are paid today, and dues for the second year are payable one year from today. However, the ADLA also has an option for members to buy a lifetime membership today for $5, 000 and never have to pay annual membership dues. Obviously, the lifetime membership isn't a good deal if you only remain a member for a couple of years, but if you remain a member for 40 years, it's a great deal. Suppose that the appropriate annual interest rate is 7.5%. What is the minimum number of years that Lloyd must remain a member of the ADLA so that the lifetime membership is cheaper (on a present value basis) than paying $550 in annual membership dues? (Note: Round your answer up to the nearest year.) 16 years 21 years 18 years 14 years In 1626, Dutchman Peter Minuit purchased Manhattan Island from a local Native American tribe. Historians estimate that the price he paid for the island was about $24 worth of goods, including beads, trinkets, cloth, kettles, and axe leads. Many people find it laughable that Manhattan Island would be sold for $24, but you need to consider the future value (FV) of that price in more current times. If the $24 purchase price could have been invested at a 6% annual interest rate, what is its value as of 2012 (386 years later)? $119, 589, 805, 520.28 $161, 797, 972, 174.50 $185, 715, 933, 278.55 $140, 693, 888, 847.36

Explanation / Answer

1) Answer: 14 years.

Calculation:

The PV of the life membership fee = $5000

As long as the PV of the annual payments of $550 is less than $5000, it is economical to pay the yearly fee.

If both have the same PV, we have the following equality:

5000 = 550*pvifa (annuity due)(7.5,n)

9.0909 = pvifa (annuity due)(7.5,n)

From the interest factor table for annuity due, the factor of 9.090 for 7.5% is relevant for 14 years.

2) FV after 386 years = 24*1.06^386 = $140,693,888,847.36

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