The amount of interest earned on A for one year is $336, while the equivalent amount of discount is $300. Find A.

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- Sep 5th 2007, 01:08 PMJrb599Rate of Discount
The amount of interest earned on A for one year is $336, while the equivalent amount of discount is $300. Find A.

- Sep 15th 2007, 05:39 AMScottO

You could create 2 simultaneous equations with 2 unknowns: $\displaystyle A$ and the interest/discount rate, call it $\displaystyle i$. The trick is putting $\displaystyle i$ in the right terms so it cancels when combining the 2 equations.

For example, one equation...

$\displaystyle A(1 + i) = 336$

After reading TKHunny's response, I see I left a piece of my equation out!! Previous should be...

$\displaystyle A(1 + i) = A + 336$

Sorry.

Hopefully this heads you in the right direction...?

-Scott - Sep 16th 2007, 01:56 PMTKHunny
The important idea here is the difference between interest and discount processes.

Let's talk about short-term loans.

For Interest, you get A and pay back (A+Interest) later.

For Discount, you get (A-Discount) and pay back A later.

This leads to two structures. If 'i' is the rate if interest or discount...

Interest: A(1+i) = A + Interest

Discount: (A - Discount)(1+i) = A

In this case, we know two of the values, the Interest and the Discount:

Interest: A(1+i) = A + 336

Discount: (A - 300)(1+i) = A

Solve for A and i.