An algebra problem by Engin Akpinar

The simplest way to solve this problem (and the key way to avoid making mistakes with the algebra) is to simply plug in your own numbers for a, r and y. If we keep it simple, let us say that the loan amount a is 100 dollars, the interest rate r is 0.1, and the length of the loan is 2 years. Now we can find our initial p.

$p= .5ary+a 12y$

$p= .5(100)(0.1)(2)+100 12(2)$

$p= 110 24$

$p=4.58$

Now if we leave everything else intact, but double our loan amount (a value), we get:

$p= .5ary+a 12y$ $p= .5(200)(0.1)(2)+200 12(2)$

$p= 220 24$

$p=9.16$

When we doubled our a value, our p value also doubled.

Our final answer is,p is multiplied by 2

By the equation we know that

$p \propto a$

$\implies$ If $a$ is doubled, $p$ is also doubled.