A certain loan was returned in two equal half - yearly instalments each of Rs. 6,760. If the rate of interest was 8% p.a., compounded yearly, how much was the interest paid on the loan?
Rs. 770
With half-yearly instalments, take the per-period rate as \(\tfrac{8\%}{2}=4\%\). The principal equals the present value of the two instalments at 4% per half-year.
\[P=\frac{6760}{1.04}+\frac{6760}{(1.04)^2}=6500+6250=12750\]
Total interest:
\[\text{Interest}=2\times 6760-12750=13520-12750=770\]
Therefore the interest paid is Rs. 770.
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