A sum of money amounts to ₹16,800 in one year and to ₹17,472 in one and a half years on the basis of interest compounded semi-annually. What is the rate of interest per annum?

When compounded semi-annually, interest is calculated every 6 months (half-year).
The duration from 1 year to 1
2
1
​
years is exactly one half-year period.

Amount at 1 year (A
2
​
after 2 half-years) = ₹16,800
Amount at 1.5 years (A
3
​
after 3 half-years) = ₹17,472

The interest earned in this half-year period is:

Interest=17472−16800=₹672
Let R
half
​
be the rate of interest per half-year. This interest is earned on the principal amount of ₹16,800:

672=
100
16800×R
half
​
×1
​

672=168×R
half
​

R
half
​
=
168
672
​
=4%
Since R
half
​
is the semi-annual rate, the annual rate of interest (R) is:

R=2×R
half
​
=2×4%=8%