Question

if the principal is 2400 and the time is 6 months and over that 6 months you gained 42 dollars what would be the annual rate​

Answer 1

The annual interest rate is 3.5%. This is calculated by finding the rate that, over 6 months, results in a $42 gain on a $2400 principal investment.

To determine the annual interest rate, we can use the formula for simple interest:

`\[ \text{Simple Interest} = P \cdot r \cdot t \]`

Where:

- P is the principal amount (initial investment),

- r is the annual interest rate (as a decimal),

- t is the time the money is invested or borrowed in years.

Given that the principal ( P ) is $2400, the time ( t ) is 6 months (which is
`(\( (1)/(2) \) year)`, and the interest gained is $42, we can substitute these values into the formula:

`\[ 42 = 2400 \cdot r \cdot (1)/(2) \]`

Now, solve for r :

`\[ r = (42 \cdot 2)/(2400) \]`

`\[ r = (84)/(2400) \]`

r = 0.035

To express the annual rate as a percentage, multiply by 100:

`\[ r_{\text{annual}} = 0.035 * 100 = 3.5\% \]`

Therefore, the annual interest rate is 3.5%.