Question

Luther made $9,000 in interest by placing $60,000 in a savings account with simple interest for 3 years. What was the interest rate?

Answer 1

`5\%\text{ or }0.05`

Explanation:

Simple interest rate means if I have "P" amount that I initially deposited, then every year this amount increases by "x% of P" or the original amount I deposited. So it's increasing by the same amount each year, unlike compound interest.

The formula for calculating the amount of interest is:
`I=P*r*t`

Where, r is the interest rate, t is the time unit, and P is the initial amount.

In most cases the t will be expressed in years, and one thing to note is the r is the interest rate in decimal form, so
`30\%=0.30`, we want to convert it to decimal form by dividing by 100

We know the amount of interest, as it's given to us as 9,000, and the principle amount or initial amount, given to us as 60,000, and also the time which is given to us as 3 years.

So we know that:

`I=9,000\\P=60,000\\t=3\\`

Plugging all these values into the equation we get:

`9,000=60,000*3*r\\\\9,000=180,000*r\\\\(9,000)/(180,000)=r\\\\0.05=r`

as noted above, this interest rate, "r" is expressed in decimal form. Since we have to divide by 100 to convert from percentage to decimal, we have to multiply by 100 to convert from decimal to percentage.

this gives us:
`r=5\%`