Question

The Morgan silver dollar has a mass of \(26.73 \mathrm{~g}\). By law, it was required to contain \(90 \%\) silver, with the remainder being copper. (a) When the coin was minted in the late 1800s, silver was worth \(\$ 1.18\) per troy ounce (31.1 g). At this price, what is the value of the silver in the silver dollar? (b) Today, silver sells for about \(\$ 13.25\) per troy ounce. How many Morgan silver dollars are required to obtain \(\$ 25.00\) worth of pure silver?

Short answer

The mass of silver in the Morgan silver dollar is \(24.057 \mathrm{~g}\). In the late 1800s, the value of the silver in the coin was $0.91. Today, the value of the silver in the coin is $10.46. To obtain $25 worth of pure silver today, you would need 3 Morgan silver dollars.

Step-by-step solution

Calculate the mass of silver in the silver dollar

The mass of the Morgan silver dollar is 26.73 grams, and it contains 90% silver. We can find the mass of silver in the coin by multiplying the mass of the coin with the percentage of silver: Mass of silver = Mass of Morgan dollar × (Silver percentage / 100) Mass of silver = \(26.73 \mathrm{~g} \times (\frac{90}{100})\) Mass of silver = \(24.057 \mathrm{~g}\)

Calculate the value of the silver in the late 1800s

In the late 1800s, silver was worth 1.18 dollars per troy ounce (31.1 grams). We can find the value of the silver in the coin using this price and the mass of silver we found in Step 1: Value of silver (late 1800s) = \(\frac{Mass \ of \ silver \times Price \ per \ troy \ ounce}{troy \ ounce \ in \ grams}\) Value of silver (late 1800s) = \(\frac{24.057 \mathrm{~g} \times \$1.18}{31.1 \mathrm{~g}}\) Value of silver (late 1800s) = $0.91

Calculate the value of the silver today

Today, silver is worth 13.25 dollars per troy ounce (31.1 grams). We can find the value of the silver in the coin using this price and the mass of silver from Step 1: Value of silver (today) = \(\frac{Mass \ of \ silver \times Price \ per \ troy \ ounce}{troy \ ounce \ in \ grams}\) Value of silver (today) = \(\frac{24.057 \mathrm{~g} \times \$13.25}{31.1 \mathrm{~g}}\) Value of silver (today) = $10.46

Calculate how many Morgan silver dollars are needed for $25 worth of silver today

We know the value of the silver in a Morgan dollar today and want to find how many coins are needed to get $25 worth of silver. We can use this equation: Number of coins = \(\frac{Amount \ of \ silver \ needed}{Value \ of \ silver \ per \ coin}\) Number of coins = \(\frac{\$25}{\$10.46}\) Number of coins = 2.39 The answer is not a whole number, but you cannot have a fraction of a coin. Therefore, you would need 3 Morgan silver dollars to get $25 worth of pure silver today.

Key concepts

Silver Dollar Composition

The Morgan Silver Dollar is noted for its historical value and unique composition. This coin was composed of two metal elements: silver and copper.
By design, each Morgan dollar contained

• 90% Silver - providing valuable metal content
• 10% Copper - to increase durability

The total mass of these coins is precisely 26.73 grams. To understand the significance of this, one must recognize the premium placed upon silver even during its minting. The silver content constituted most of the coin's intrinsic value. This specific composition was mandated, ensuring consistency in both the coin's appearance and value through its years of production. As such, the Morgan dollar serves as a fascinating snapshot of historical currency practices.

Mass Percentage Calculation

Calculating the mass percentage of the components in a coin like the Morgan Silver Dollar helps us understand its material worth. The exercise requires determining how much silver exists in this silver dollar.
Using the percentage given, you multiply:

• Total mass of the coin: 26.73 grams
• Percentage of silver content: 90%

This calculation follows the formula:\[ \text{Mass of silver} = 26.73 \times \left( \frac{90}{100} \right) \]The outcome is 24.057 grams of silver in each coin. Understanding this step equips you with the ability to deduce the proportion of valuable metal in any similar alloy-based coin.
This concept is foundational in determining the overall market value of these types of historical currencies, especially when factoring in changes in silver's worth over time.

Historical Silver Prices

The market value of silver has long been an indicator of economic conditions, and it varies significantly over time. In the late 1800s, silver was priced at \( \\(1.18 \) per troy ounce. A troy ounce equals 31.1 grams, a standard unit for precious metals.
This historical price point enables us to calculate the contemporary value of silver within a coin during its minting period. The formula needed:

• Mass of silver in the coin (24.057 grams)
• Price of silver: \( \\)1.18 \) per troy ounce

Using:\[ \text{Value of silver} = \frac{24.057 \times 1.18}{31.1} = \\(0.91 \]The silver content in a Morgan dollar was worth approximately \\)0.91 at the time of minting. This highlights how historical prices reflect the economic climate and resource accessibility during different periods, thus affecting coin values in the past.

Modern Silver Valuation

Today, the silver market has changed dramatically compared to the late 1800s. Modern rates have seen silver soar to \( \\(13.25 \) per troy ounce. This dramatically increases the coin's value based on its silver content alone.
The steps to calculate today’s value are similar, applying the current price to the coin’s silver mass:

• Mass of silver: 24.057 grams
• Today's silver price per troy ounce: \( \\)13.25 \)

Apply the calculation:\[ \text{Modern value of silver} = \frac{24.057 \times 13.25}{31.1} = \\(10.46 \].
This means the silver in one Morgan silver dollar is worth \\)10.46 today. Understanding modern valuation not only showcases inflation but also the fluctuating demand and investment value of precious metals like silver, altering the intrinsic worth of historical coins.