# Rate of Discount

• Sep 5th 2007, 01:08 PM
Jrb599
Rate 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 AM
ScottO
Quote:

Originally Posted by Jrb599
The amount of interest earned on A for one year is \$336, while the equivalent amount of discount is \$300. Find A.

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 PM
TKHunny
Quote:

Originally Posted by Jrb599
The amount of interest earned on A for one year is \$336, while the equivalent amount of discount is \$300. Find A.

The important idea here is the difference between interest and discount processes.

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.