In how much time (in years) will ₹8,000 amount to ₹9,159.20 at 14% per annum interest compounded half yearly?

Given:
Principal (P) = ₹8,000

Amount (A) = ₹9,159.20

Annual Rate (R) = 14%

Since the interest is compounded half-yearly:

Rate per half-year (R
′
) =
2
14%
​
=7%=0.07

Let n be the number of half-yearly periods.

The compound interest formula is:

A=P(1+
100
R
′

​
)
n

9,159.20=8,000×(1+0.07)
n

8,000
9,159.20
​
=(1.07)
n

80,000
91,592
​
=(1.07)
n

Divide both numerator and denominator by 8,000:

80,000÷8
91,592÷8
​
=
10,000
11,449
​
=1.1449
So we have:

1.1449=(1.07)
n

Since (1.07)
2
=1.1449, it follows that:

n=2half-yearly periods
Converting half-yearly periods into years:

Time=
2
2
​
=1year