Question
At what rate per annum will 400 Naira youth 50 naira interest in two whole number 1/2 years
Answers
GPT-4o mini
To find the annual interest rate that would yield 50 Naira in interest from an investment of 400 Naira over a period of 2.5 years, you can use the formula for simple interest:
\[
I = P \times r \times t
\]
Where:
- \( I \) = interest earned (50 Naira)
- \( P \) = principal amount (400 Naira)
- \( r \) = annual interest rate (in decimal)
- \( t \) = time (in years, which is 2.5 years)
Now, we can rearrange the formula to solve for \( r \):
\[
r = \frac{I}{P \times t}
\]
Substituting the known values:
\[
r = \frac{50}{400 \times 2.5}
\]
Now calculate the denominator:
\[
400 \times 2.5 = 1000
\]
So now the equation becomes:
\[
r = \frac{50}{1000} = 0.05
\]
To express \( r \) as a percentage, multiply by 100:
\[
r = 0.05 \times 100 = 5\%
\]
Therefore, the annual interest rate is **5% per annum**.
\[
I = P \times r \times t
\]
Where:
- \( I \) = interest earned (50 Naira)
- \( P \) = principal amount (400 Naira)
- \( r \) = annual interest rate (in decimal)
- \( t \) = time (in years, which is 2.5 years)
Now, we can rearrange the formula to solve for \( r \):
\[
r = \frac{I}{P \times t}
\]
Substituting the known values:
\[
r = \frac{50}{400 \times 2.5}
\]
Now calculate the denominator:
\[
400 \times 2.5 = 1000
\]
So now the equation becomes:
\[
r = \frac{50}{1000} = 0.05
\]
To express \( r \) as a percentage, multiply by 100:
\[
r = 0.05 \times 100 = 5\%
\]
Therefore, the annual interest rate is **5% per annum**.