To find out the actual manufacturing value of a coin, I will add the cost of copper and zinc.
For copper:
6.90 ÷ 1000 = $0.0069 per gram of copper
For 0.071 grams, the price would be:
0.0069 x 0.071 = $0.0004899 for the mass of copper in a coin
For zinc:
1.75 ÷ 1000 = $0.00175 per gram of zinc
For 2.764 grams, the price would be:
0.00175 x 2.764 = $0.004837 for the mass of zinc in a coin
For the total price of both metals in a coin:
0.0004899 + 0.004837 = $0.0053269 or 0.53269 cents
Since the metal value is less than 1 cent, it is not worth melting as the face value of the coin is still higher than the metal value.
6. The 1 and 2 Euro coins are composed of copper-nickel, nickel-brass and nickel. The reason these metals were used are because they wanted the coin to be difficult to forge considering its high value.
The 10, 20 and 50 cent coins are made up of something called Nordic Gold. Nordic Gold consists of 89% copper, 5% aluminum, 1% zinc and some tiny amounts of other metals. By using all of these metals, Nordic Gold is hard to produce and this reduces the chances of counterfeit.
The 1, 2 and 5 cent Euro coins are made of copper-plated steel and have a reddish appearance. The material is relatively cheap to produce and can be processed in the coin press without any problems. The coin is also protected against oxidation by the copper layer.
7. For this question, I will pick only on coin to calculate the value of the metal and see if it is worth melting them. I picked the 50 cent Euro coin.
Composition of 50 cent Euro coin:
- 89% copper
- 5% aluminum
- 5% zinc
- 1% Tin
Price of metals (as of 21st October, 2011)
- Copper: $6.917 per kilogram
- Aluminum: $2.122 per kilogram
- Zinc: $1.75 per kilogram
- Tin: $21.35 per kilogram
Mass of metals in 50 cent Euro coin (Mass of 50 cent Euro coin = 7.8 grams):
- Copper: 7.8 x 0.89 = 6.942 grams
- Aluminum: 7.8 x 0.05 = 0.39 grams
- Zinc: 7.8 x 0.05 = 0.39 grams
- Tin: 7.8 x 0.01 = 0.078 grams
Price of metals in 50 cent Euro coin:
-
Copper: 0.006917 x 6.942 = $ 0.048017814 or 0.0346666 EUR (0.0346 EUR)
-
Aluminum: 0.002122 x 0.39 = $ 0.00082758 or 0.000598738 EUR (0.0006 EUR)
-
Zinc: 0.00175 x 0.39 = $0.0006825 or 0.000493840 EUR (0.0005 EUR)
- Tin: 0.02135 x 0.078 = $0.0016653 or 0.00119845 EUR (0.0012 EUR)
Value of all the metals:
0.0346 + 0.0006 + 0.0005 + 0.00012 = 0.0369 EUR
The face value of a 50 cent Euro coin is 0.50 EUR. The value of all the metals combined come around to 0.0369 EUR and this is significantly lower than the face value of the coin. Hence, it is not worth melting the Euro coins.
8. The degree of accuracy is pretty high. In some parts I did not round up to make the answer more accurate. For example, in question 7, I did not round up the dollars or the euros because I wanted them to be accurate as possible when I add them up to the total value of the metal. In other questions such calculations, I tried to round up to the third decimal place to make the calculations easier. If I did not round them up, the number becomes too long and it will become harder to use them in calculations. Sometimes I let the number go to the 4th decimal place if the number is too small such as 0.00015 grams. If I rounded that up to 0.0002 grams, it would mess up my calculations and so I left it at the 4th decimal place.
9. In the short term run, I think that the prices of the metals will fluctuate a lot and at some points, the metal value will go higher than the face value especially due to inflation and economic recessions. The government will try to fix this by coming up with different compositions of metals and will use more of cheaper metals. At some points the face value might be worth more than the metal value but no one can predict the near future since the prices will be varying a lot. In the long term run, the metals will become scarcer and soon the price of the metals will increase making the metal value worth more than the face value. At this point, the government will have to decrease the distribution of these coins.
10.
a) The methods that I used are correct and I know this as most of them are simple and only require logic. Since I do not see any error in my calculations and all of my findings make sense, I know that I did not make an error in the process of finding the answer and that my method of the finding the answer is correct.
b) My findings are reliable as I used a calculator to do all of my calculations to make sure nothing is wrong. I also double checked all of my methods and calculations to make sure that I did not make an error anywhere. If I made an error in a crucial part, it would result in my making an error in all of my other calculations so I was very careful with my calculations. I also checked on the internet just as a back-up if my answer if actually correct. I took all of the data that I needed from trusted websites that regularly update the prices of metals.
c) The ratio of the metal value to the face value was different for the penny was different from the euro coins. In the case of the penny, the metal value was a little over half the face value whereas for the Euro coin, there is a big difference between the metal value and face value.
d) There are quite a few improvements that I can make especially in the calculations.
11. Rise in Metal Prices Could Mean Shortage of Coins
Fueled by the increasing scarcity of metals, the prices of metals have been increasing and show no sign of slowing down. At this rate, people might start melting down their coins for scrap.
For example, the penny which is the smallest denomination of the US currency is currently worth about 0.53 cents at the current metal prices. An increase in the metal prices of zinc and copper could cause the metal value of the penny to rise above its face value of 1 cent. In this case, people would start melting their coins in large numbers and selling the metal as scrap and making a decent profit in the process. However, at the rate that metal prices have been climbing, this might actually become true. Experts suggest that the prices of metals will keep increasing and that we should wait before we melt them.
Other currencies such as the Euro do not face this problem. Their metal value remains far below the face value and therefore keeping them safe from being melted. This is due to combinations of right compositions of metals in the Euro coins. They use many alloys and many different metals to make it harder to produce counterfeit coins yet they are able to keep the metal value below the face value which is a remarkable feat.
In the short run, the metals will keep getting more expensive. Management at Freeport-McMoRan Copper and Gold (FCX), the world’s largest publicly traded copper company, claims that the demand for physical copper is looking stronger than it has for a very long time.
According to some experts, the increasing prices of copper could potentially prompt a switch to aluminum whose prices have been quite stable. As the CEO of FCX Richard Adkerson puts it, “They're concerned about high copper prices because of...the potential substitution, but offsetting that substitution is new markets". `
In the long run, prices are expected to soar due to the excess demand and scarcity of metals created by booming industrial cities. Due to this, governments will face a tough time preventing people from melting coins and that they should come up with better compositions of coins.
Bibliography: "Report: Record Copper Prices Prompt Switch to Aluminum - Seeking Alpha." Stock Market News & Financial Analysis - Seeking Alpha. Web. 22 Oct. 2011. <http://seekingalpha.com/article/258844-report-record-copper-prices-prompt-switch-to-aluminum>.
"Will Copper Keep Climbing Higher? | Markets | Minyanville.com." Minyanville -- Stock Market, Investment, Finance, Money, Hoofy & Boo. Web. 22 Oct. 2011. <http://www.minyanville.com/businessmarkets/articles/copper-red-metal-ipath-copper-fund/7/22/2010/id/29270>
Part 2
1.
- Same basic shapes are shapes that are similar to each other. The dimensions of 2 objects might vary proportionally (by an enlargement factor) but if they have the same basic shape, they are still similar to each other.
-
A coin is basically a cylinder. To find the volume of a cylinder, we can use this formula: V=πr2h or Volume = Pi x radius2 x height (in this case thickness). To find the volume, we only need two dimensions, the radius and the height and both are given to us. So all we have to do is to insert these into the equation. Note: In all of the equations, I will take Pi as 3.14.
V=πr2h
V = 3.14 x 102 x 1.2
= 94,2mm3
Hence, the volume of the 10 cent coin is 94.2mm3.
- The 10 cent and the 20 cent coin are two similar solids and we have the volume for both. With this information, we can apply the formula below to find one of the dimensions of the 20 cent coin.
First, we have to find the volume of the 20 cent coin. Since the questions states that the 20 cent coin’s volume will be double the 10 cent coin’s volume, we can calculate the volume like this: 94.2 x 2 = 188.4 mm3
Therefore, the ratio between the two thicknesses of the 20 cent coin to the 10 cent coin would be 1.5 : 1.2 or 1.25 which is the enlargement factor.
-
From the article, we know that the 20 cent coin will have double the volume of the 10 cent coin. We have the volume of the 10 cent coin and hence we find the volume of the 20 cent coin by this calculation: 94.2 x 2 = 188.4mm3.
We already have the thickness of the coin which is 1.5mm and we also have the volume and so now we can find the thickness.
V=πr2h
188.4 = 3.14 x 1.5 x r2
188.4 = 4.71 x r2
r2 = 40
r =
r = 6.32455532mm or 6.3mm
Diameter = radius x 2
Diameter = 6.3 x 2
Diameter = 12.6mm
Hence, the volume of the coin is 188.4mm3, the diameter is 12.6mm and the thickness is 1.5mm.
- For 50 cent coin:
Volume of 20 cent coin : Volume of 50 cent coin = 2 : 5
Therefore, Volume of 50 cent coin = 188.4 x = 471mm3
To find the dimensions, we need to calculate at least one dimension using the method I used earlier.
Diameter: V = πr2h
471 = 3.14 x r2 x 2.1
71 = r2
r = 8.45 mm
Diameter = 8.45 x 2 = 16.9mm
Hence, the volume of the coin is 471mm3, the diameter is 16.9mm and the thickness is 2.1mm.
For 1 dollar coin:
Volume of 50 cent coin : Volume of 1 dollar coin = 1 : 2
Therefore, Volume of 1 dollar coin = 471 x 2 = 942mm3
To find the dimensions, we need to calculate at least one dimension using the method I used earlier.
Diameter: V = πr2h
942 = 3.14 x r2 x 2.6
115 = r2
r = 10.7 mm
Diameter = 10.7 x 2 = 21.4mm
Hence, the volume of the coin is 942mm3, the diameter is 21.4mm and the thickness is 2.6mm.
4 Different Compositions of Coins
