A coin sold at auction in 2017 for $3,158,000. The coin had a face value of $2 when it was issued in 1786 and had previously been sold for $420,000 in 1971. a. At what annual rate did the coin appreciate from its first minting to the 1971 sale? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e. g., 32.16.) b. What annual rate did the 1971 buyer earn on his purchase? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e. g., 32.16.) c. At what annual rate did the coin appreciate from its first minting to the 2017 sale? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e. g., 32.16.)

A) future value = present value (1 + rate)ⁿ

420,000 = 2 (1 + r)¹⁸⁵

420,000 / 2 = (1 + r)¹⁸⁵

210,000 = (1 + r)¹⁸⁵

¹⁸⁵√210,000 = 1 + r

1.06848 = 1 + r

1.06848 - 1 = r

r = 0.06848 or 6.85%

B) future value = present value (1 + rate)ⁿ

3,158,000 = 420,000 (1 + r)⁴⁶

3,158,000 / 420,000 = (1 + r)⁴⁶

7.519 = (1 + r)⁴⁶

⁴⁶√7.519 = 1 + r

1.04483 = 1 + r

1.04483 - 1 = r

r = 0.04483 or 4.48%

C) future value = present value (1 + rate)ⁿ

3,158,000 = 2 (1 + r)²³¹

3,158,000 / 2 = (1 + r)²³¹

1,579,000 = (1 + r)²³¹

²³¹√1,579,000 = 1 + r

1.0637 = 1 + r

1.0637 - 1 = r

r = 0.0637 or 6.37%

in 2001, dell computer became the world’s largest personal computer vendor, continuing to

gain market share and post profits in an industry struggling with slumping sales and billions of

dollars in losses. dell sells 90% of its pcs directly to the final customer, largely bypassing the

reseller channel that accounts for most of the world’s pc sales. this direct customer relationship

is the key to dell’s business model, and provides distinct advantages over the indirect sales

model. dell’s direct relationship with the customer allows it to tailor its offerings to customer

needs, offer add-on products and services, and use the internet to offer a variety of customer

services. in addition, dell’s pcs are built to customers’ specifications upon receipt of an order,

giving dell additional advantages over indirect pc vendors who must try to forecast demand and

ship products based on those forecasts. dell’s direct sales and build-to-order model has achieved

superior performance in the pc industry in terms of inventory turnover, reduced overhead, cash

conversion, and return on investment (kraemer, et al., 2000).

explanation: