**Given:**
Principal amount (P) = ₹25600
Amount after ‘t’ years (A) = ₹36450
Rate of interest (R) = 25% p.a. compounded semi-annually

**To find:** The value of ‘t’

**Formula:** The compound interest formula is given by:

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

Where:
A = Amount after ‘t’ years
P = Principal amount
R = Rate of interest
n = Number of times interest is compounded per year
t = Time in years

**Solution:**

Step 1: Given that the interest is compounded semi-annually, we need to find the effective rate of interest for each half-year.

Rate of interest per half-year (r) = R/2 = 25%/2 = 12.5%

Step 2: Substitute the given values in the compound interest formula:

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

₹36450 = ₹25600(1 + 12.5%/2)^(2t)

Step 3: Simplify the equation:

(1 + 12.5%/2)^(2t) = ₹36450/₹25600

(1 + 0.125/2)^(2t) = 36450/25600

(1 + 0.0625)^(2t) = 1.42578

(1.0625)^(2t) = 1.42578

Step 4: Take the logarithm of both sides to solve for ‘t’:

log[(1.0625)^(2t)] = log(1.42578)

2t * log(1.0625) = log(1.42578)

t = log(1.42578) / (2 * log(1.0625))

Using a calculator, we can find the value of ‘t’ as follows:

t ≈ 3.5 years

Therefore, the value of ‘t’ is approximately 3.5 years.