Questions: How much should you invest at 3.5% simple interest in order to earn 50 interest in 5 months?

Solution Steps

We are given the following values:

• Interest earned, \( I = 50 \)
• Interest rate, \( R = 3.5\% = \frac{3.5}{100} = 0.035 \)
• Time period, \( T = 5 \text{ months} = \frac{5}{12} \text{ years} \)

The simple interest formula is given by: \[ I = PRT \] We need to rearrange this formula to solve for the principal \( P \): \[ P = \frac{I}{RT} \]

Substituting the known values into the rearranged formula: \[ P = \frac{50}{0.035 \times \frac{5}{12}} \]

Now, we calculate the principal: \[ P = \frac{50}{0.035 \times \frac{5}{12}} = \frac{50}{\frac{0.175}{12}} = \frac{50 \times 12}{0.175} = \frac{600}{0.175} \] Calculating this gives: \[ P = 3428.57 \]

Thus, the principal amount needed is \( P \approx 3428.57 \).

Final Answer