Find the principle, given r=3% and t=3/4 years, a=2556.25

What does a represent?

PRINCIPAL , not principle (they sound the same but are very different)

Now you do not say but I suppose you are doing continuous compounding for 0.75 years at 3% ????

If so

A = P e^(rt)
here A = 2556.25
r = 0.03
t = 0.75

2556.25 = P e^(.0225)
2556.25 = P * 1.02276

LCM 26, 6

44,5

To find the principle (P), we can use the formula for calculating compound interest:

A = P * (1 + r/n)^(n*t)

Where:
A = the final amount (also known as the future value)
P = the principle (initial amount)
r = the interest rate
t = the time in years

In this case, we are given:
r = 3% (which is equal to 0.03 as a decimal)
t = 3/4 years (or 0.75 years)
A = 2556.25

We need to rearrange the formula to solve for P. Dividing both sides of the equation by the expression (1 + r/n)^(n*t), we can isolate P:

P = A / (1 + r/n)^(n*t)

Assuming the interest is compounded annually (n = 1), we can substitute the given values into the formula:

P = 2556.25 / (1 + 0.03/1)^(1 * 0.75)

Simplifying further:

P = 2556.25 / (1 + 0.03)^(0.75)

P = 2556.25 / (1.03)^0.75

P ≈ 2485.61

Therefore, the principle (P) is approximately 2485.61.