Mr. Rao bought 1-year, ₹10000 certificate of deposit that paid interest at an annual rate of 8% compounded semi-annually. The interest received by him on maturity is

1. ₹816

2. ₹864

3. ₹800

4. ₹10816

Rate = 8% i.e. $\dfrac{8\%}{2}$ = 4% when compounded semi-annually.

n (no. of conversion periods) = 2 half-years.

C.I. = $P\Big[\Big(1 + \dfrac{r}{100}\Big)^n - 1\Big]$

Putting values in formula we get,

$C.I. = ₹10000 \times \Big[\Big(1 + \dfrac{4}{100}\Big)^2 - 1\Big] \\[1em] = ₹10000 \times \Big[\Big(\dfrac{104}{100}\Big)^2 - 1\Big] \\[1em] = ₹10000 \times \Big[\Big(\dfrac{52}{50}\Big)^2 - 1\Big] \\[1em] = ₹10000 \times \Big[\dfrac{2704}{2500} - 1\Big] \\[1em] = ₹10000 \times \dfrac{2704 - 2500}{2500} \\[1em] = ₹10000 \times \dfrac{204}{2500} \\[1em] = ₹\dfrac{2040000}{2500} \\[1em] = ₹816.$

Hence, Option 1 is the correct option.