Question

Lloyd 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 $600 per year and must be paid at the beginning of each year. For instance, membership dues for the first year are paid today, a 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. ship 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 7.4%. 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 $600 in annual membership dues? (Note: Round your answer up to the nearest year.) O 12 years O 14 years 19 years O 21 years Bry 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 5.75% annual interest rate, what is its value as of 2012 (386 years later)? $56,550,493,062.84 $48,067,919,103.42 $65,033,067,022.28 $74,646,650,842.97

Answer 1

Question 1:

1- (1 + i)- PV of an Annuity Due =R*- i *(1 + i)

$5,000 = 600 * [\frac{1-(1+0.074)^{-n}}{0.074}] * (1 + 0.074)$

$5,000 = 600 * [\frac{1-(1.074)^{-n}}{0.074}] * (1.074)$

1.074^-n = 0.425822

Taking log of both sides,

-n * LN(1.074) = LN(0.425822)

-n * 0.07139 = -0.85373

n = 11.96 years

n = 12 years

Question 2:

This question requires application of basic time value of money function, according to which FV = PV * (1 + r)" where FV is Future Value, PV is present value, n is number of periods and r is rate per period

FV = 24 * (1 + 0.0575)³⁸⁶

FV = 24 * 2,356,270,544.28

FV = $56,550,493,062.83 (Option A)