Answer: The simple interest on a sum of money invested at 3% per annum for 2 1/2 years is N9.225, and the principal is N3,000.
Explanation:
We can use the formula for simple interest:
I = P * r * t
where I is the interest, P is the principal, r is the interest rate, and t is the time in years.
Given that the interest is N123, the interest rate is 3% per annum, and the time is 2 1/2 years, we can plug these values into the formula and solve for the principal:
123 = P * 0.03 * 2.5
Simplifying, we get:
123 = 0.075P
P = 123 / 0.075
P ≈ 1,640
Therefore, the principal is approximately N1,640.
However, this principal value does not correspond to the given interest amount of N9.225. To obtain the correct principal, we need to use the correct interest amount:
We can convert the time of 2 1/2 years to 5/2 years, and use the formula for simple interest:
I = P * r * t
where I is the interest, P is the principal, r is the interest rate, and t is the time in years.
Given that the interest is N9.225, the interest rate is 3% per annum, and the time is 5/2 years, we can plug these values into the formula and solve for the principal:
9.225 = P * 0.03 * 5/2
Simplifying, we get:
9.225 = 0.0375P
P = 9.225 / 0.0375
P = 246
Therefore, the principal is N246.