3. mika opened a bank account that earns simple interest with an initial deposit of $2,200. she made no…

3. mika opened a bank account that earns simple interest with an initial deposit of $2,200. she made no other transactions throughout the year. at the end of the year, mika had $2,260.50 in her account. what was the simple interest rate?

3. mika opened a bank account that earns simple interest with an initial deposit of $2,200. she made no other transactions throughout the year. at the end of the year, mika had $2,260.50 in her account. what was the simple interest rate?

Answer

Explanation:

Step1: Find the interest earned

The initial deposit (principal, ( P )) is $2200, and the final amount (( A )) is $2260.50. The interest (( I )) is the difference between the final amount and the principal. So, ( I = A - P = 2260.50 - 2200 = 60.50 ).

Step2: Recall the simple interest formula

The formula for simple interest is ( I = P \times r \times t ), where ( r ) is the annual interest rate (in decimal) and ( t ) is the time in years. Here, ( t = 1 ) year (since it's for one year).

Step3: Solve for ( r )

Substitute ( I = 60.50 ), ( P = 2200 ), and ( t = 1 ) into the formula: ( 60.50 = 2200 \times r \times 1 ). Then, solve for ( r ) by dividing both sides by 2200: ( r = \frac{60.50}{2200} = 0.0275 ).

Step4: Convert to percentage

To convert the decimal to a percentage, multiply by 100: ( r = 0.0275 \times 100 = 2.75% ).

Answer:

The simple interest rate is ( 2.75% )