The Problem:
The problem states that the compound interest on a certain sum in 2 and a half years at an annual interest rate of 10% compounded yearly is 1623.

Solution:
To find the sum, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:
A = the final amount (including interest)
P = the principal amount (initial sum)
r = the annual interest rate (as a decimal)
n = the number of times that interest is compounded per year
t = the number of years

In this case, the given information is:
Interest Rate (r) = 10% = 0.10
Time (t) = 2.5 years
Compound Frequency (n) = 1 (compounded yearly)
Compound Interest (A) = 1623

Calculation:
Let's substitute the given values into the formula and solve for P:

1623 = P(1 + 0.10/1)^(1*2.5)

Simplifying the equation further:

1623 = P(1 + 0.10)^(2.5)

1623 = P(1.10)^(2.5)

Now we need to isolate P by dividing both sides of the equation by (1.10)^(2.5):

P = 1623 / (1.10)^(2.5)

Using a calculator to evaluate (1.10)^(2.5), we find:

P ≈ 1279.74

Therefore, the principal amount (sum) is approximately 1279.74.

Conclusion:
The principal amount (sum) is approximately 1279.74.

Ans...7623