Let \( x \) be the original balance of the account. According to the information provided, after earning interest, the new balance is \( 420 \), which is a certain fraction of the original balance. However, the proportion was not provided in your question. Therefore, I will assume the new balance is a specific fraction \( r \) of the original balance.
The equation can be written as: \[ 420 = r \cdot x \]
To find \( x \), we need to rearrange the equation: \[ x = \frac{420}{r} \]
Now, we need to know the value of \( r \) to proceed further. If you have a specific fraction or percentage in mind, please provide it.
Assuming \( r = 1.05 \) (which means the account has increased by 5%): \[ x = \frac{420}{1.05} \approx 400 \]
Now, to find the interest earned: \[ \text{Interest} = \text{New Balance} - \text{Original Balance} = 420 - 400 = 20 \]
So, assuming \( r = 1.05 \):
- The original balance of the account was approximately $$400.
- The account earned $$20 in interest.
If you have a different fraction or ratio for the interest, please provide it, and I can adjust the calculations accordingly.