To find the rate of simple interest, we can use the formula for simple interest:
\[ I = P \times r \times t \]
where:
- \( I \) is the interest earned (₦21.00),
- \( P \) is the principal amount (₦280),
- \( r \) is the rate of interest (expressed as a decimal),
- \( t \) is the time in years (2.5 years).
We need to rearrange the formula to solve for the rate \( r \):
\[ r = \frac{I}{P \times t} \]
Now, plug in the values:
\[ I = 21.00 \] \[ P = 280 \] \[ t = 2.5 \]
Substituting the values into the formula, we get:
\[ r = \frac{21}{280 \times 2.5} \]
Calculating the denominator:
\[ 280 \times 2.5 = 700 \]
Now we can calculate \( r \):
\[ r = \frac{21}{700} = 0.03 \]
To express \( r \) as a percentage, we multiply by 100:
\[ r = 0.03 \times 100 = 3% \]
Therefore, the rate at which ₦280 will earn ₦21.00 in simple interest for 2 1/2 years is 3%.