A ratio of one value to another value should not have units (i.e. we should not need to specify a currency unit, such as dollars), as both values can be expressed in terms of dollars and the units should cancel. However, both face value and intrinsic value must be expressed in terms of the same currency; Australian dollar unit doesn’t cancel the U.S. dollar unit. We’ll use USD to signify U.S. dollars and AUD to signify Australian dollars.
Putting both values in terms of U.S. dollars:
Intrinsic value = (1 troy ounce of gold)(1775.30 USD/troy ounce of gold) = 1775.30 USD
Face Value = (100 AUD)(1.016 USD/1 AUD) = 101.60 USD
Ratio = Intrinsic/Face = 1775.30/101.60 = 17.4734252 {Use the calculator!}
Rounded to three decimal places, the correct answer is 17.473.
On any problem that requires converting from one unit of measure to another, first think about what we want to cancel. When converting from AUD to USD, we want to cancel AUD units out. Therefore, multiply by a term that has AUD in the denominator. But we must always multiply by 1, or else we’ll change the value, so the top and bottom of any fraction multipliers must be equal. We were told that 1 AUD = 1.016 USD, so (1.016 USD/1 AUD) equals 1 and also serves to cancel the AUD units in the face value calculation above.
Not to be currency biased, we could have solved in terms of AUD:
Intrinsic value = (1 troy ounce)(1775.30 USD/troy ounce)(1 AUD/1.016 USD) = 1747.34252 AUD {Use the calculator!}
Face Value = 100 AUD
Ratio = Intrinsic/Face = 1747.34252/100 = 17.4734252
Rounded to three decimal places, the correct answer is 17.473.
Woo-hoo!
You know... if you've been ignoring these math problems when I put them up every Tuesday, I really encourage you to try them. Are you afraid to be wrong? What silliness! We don't learn by avoiding risks! And hell, I'm taking as much of a risk as any of you, since I don't know the official answer to any given problem until the following week.
So what's holding you back? Give these problems a try!
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