Question

Madeline invests money in an account paying simple interest. No money is added or removed

from the investment. To find the balance after a year, she multiplies her current balance by
1.051. What percent simple interest does the account earn per year?

Answer 1

To determine the simple interest rate Madeline's account earns, we observe that multiplying the initial balance by 1.051 gives the new balance after a year. The 0.051 represents the interest rate, so the account earns 5.1% simple interest per year.

Step-by-step explanation:

Understanding Simple Interest

To determine the percent simple interest rate Madeline's account earns per year, we can reference the given information that multiplying her current account balance by 1.051 results in her balance after one year. This multiplication implies the interest rate plus the original amount, meaning that the 0.051 (1.051 - 1) represents the interest earned on the original investment over the course of the year.

Calculating Simple Interest

Using the provided examples, we can practice the simple interest formula:

Simple interest formula: Principal (P) × Interest Rate (R) × Time (T) = Interest (I)

Applying the formula to Example 1, with a deposit of $100 at a 5% interest rate held for one year:

• 
  
• $100 × 0.05 × 1 = $5

This shows the interest earned on a $100 investment at 5% simple interest for one year is $5, indicating the total balance would be $105, which is 1.05 times the original amount.

Now, following Madeline's case:

• 
  
• Original balance × (1 + Simple interest rate) = New balance after one year
• 
  
• Original balance × 1.051 = New balance after one year

Since we know the interest rate is the part that has been added to 1, in this case, 0.051 represents the interest rate. Therefore, Madeline's account earns 5.1% simple interest per year.