Question

After 4 years, $70,000 deposited in a savings account with simple interest had earned $30,800 in interest. What was the interest rate?

Use the formula i = prt, where i is the interest earned, p is the principal (starting amount), r is the interest rate expressed as a decimal, and t is the time in years.

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Answer 1

To find the interest rate \( r \) using the formula for simple interest, \( i = prt \), we start with the values provided:

- \( i = 30,800 \) (interest earned)
- \( p = 70,000 \) (principal)
- \( t = 4 \) (time in years)

We need to rearrange the formula to solve for \( r \):

\[
r = \frac{i}{pt}
\]

Now, we can substitute the known values into the equation:

\[
r = \frac{30,800}{70,000 \times 4}
\]

Calculating the denominator:

\[
70,000 \times 4 = 280,000
\]

Now substitute that back into the equation for \( r \):

\[
r = \frac{30,800}{280,000}
\]

Calculating \( r \):

\[
r = 0.110
\]

To express \( r \) as a percentage, we multiply by 100:

\[
r = 0.110 \times 100 = 11.0\%
\]

Thus, the interest rate is

\[
\boxed{11.0\%}
\]