Question

Antonio is a divorce attorney who practices law in New York City. 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 Antonio 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.)

12 years 14 years 18 years 21 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 heads. 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 4.00% annual interest rate, what is its value as of 2017 (391 years later)? $93,253,648.69 $109,710,174.93 $126,166,701.17 $144,817,430.91

Answer 1

Antonio:

if paid $550 per year annually in advance for 40 years, its present value is $7446 ($550 from year 0 to 39 discounted annuity at 7.5%)

However if you are taking a lifetime membership, you have to pay the amount of $5000 immediately, and its present value is $5000.

So obivioulsy lifetime membership is better in longer run.

However, we are asked the minimum years.

if paid $550 per year annually in advance for 12 years, its present value is $4565 ($550 from year 0 to 11 discounted annuity at 7.5%)

if paid $550 per year annually in advance for 14 years, its present value is $5016 ($550 from year 0 to 13 discounted annuity at 7.5%)

So the minimum number of years which Antonio should keep membership is 14 years so that it covers the amount of $5000.

Dutchman peter:

As time passed by, the value of money changes. The present value of money and its future value is different because of the interest factor present.

The value in year 1626 is $24 (Present value). However, every year the amount of money increases because of the interest element. So inorder to find out the value of $24 in current year terms, we should compound the amount by an annual interest rate of 4% for 391 years, and we can find out the future value.

FV = PV x (1+r)^n

=24x(1+0.04)^391 = 109710174