Below is a question from a recent SAT exam. It is a non-calculator question that would typically take a student 2-3 minutes to complete.
Juan purchased an antique that had a value of 200 dollars at the time of purchase. Each year, the value of the antique is estimated to increase 10% over its value the previous year. The estimated value of the antique, in dollars, 2 years after purchase can be represented by the expression 200a, where a is a constant. What is the value of a?
This is a compound interest question so we will use the formula for compound interest.
The A represents the final amount at the end of two years. We are told in the question this is equal to 200a. So let’s replace that first.
We also know the Principal amount P. We are told it is 200.
We also know the rate,\ r, 10% which as a decimal is 0.1.
Next, n is the number of times the amount compounds per year. In this case n is 1.
We also know that t is equal to 2, as this compounds for 2 years.
Now, we can simplify the RHS of the equation.
And Finally, we can divide both sides by 200.
So,
a=1.21
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