Reverse Plugging In: Basic Technique

Adrian took out a student loan that charges 10% annual simple interest. If Adrian paid back a total of $1,200 in interest alone during the first four years, how much was Adrian's loan in dollars?
Incorrect. [[Snippet]]
Incorrect. [[Snippet]] Did you forget to divide interest paid by Adrian by 4? Read the question carefully: Adrian paid $1,200 in interest over __four__ years.
Incorrect. [[Snippet]]
Incorrect. [[Snippet]]
Correct. [[Snippet]] Given that Adrian paid $1,200 in interest over four years and the annual rate of interest is 10%, the principal amount can be calculated as follows: >Interest $$=$$ Principal Amount $$\times$$ Interest Rate $$\times$$ Time >$$\rightarrow 1{,}200 =$$ Principal $$\times10% \times 4$$ >$$\rightarrow 1{,}200 =$$ Principal $$\times (\frac{10}{100}) \times 4$$. Then solve for the principal. >$$\rightarrow$$ Principal $$= 1{,}200 \times (\frac{100}{10}) \times (\frac{1}{4})$$ >$$\rightarrow$$ Principal $$= 300 \times 10$$ >$$\rightarrow$$ Principal $$= 3{,}000$$. Hence, this is the correct answer. __Alternative Method__: Numbers in the answer choices and in the specific question? Use __Reverse Plugging In__. Plug the answers back into the question. Suppose answer choice B of $3,000 were the size of Andrew's original loan. The 10% simple interest will add $300 every year (or $1,200 over 4 years). Since this fits the premises of the question, B is indeed the right answer choice.
$1,000
$3,000
$4,000
$6,000
$12,000

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