What is the compound interest if K500 is invested for a year at 2% p.a. compounded half years.?

To calculate the compound interest for an investment of K500 at 2% p.a. compounded half-yearly for one year, we can use the formula:

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

Where:
A = the future value of the investment
P = the principal amount (K500)
r = the annual interest rate (2% or 0.02)
n = the number of times the interest is compounded per year (2 for half-yearly)
t = the number of years the money is invested for (1 year)

Plugging in the values:

A = K500(1 + 0.02/2)^(2*1)
A = K500(1 + 0.01)^2
A = K500(1.01)^2
A = K500(1.0201)
A = K510.05

Now, we can calculate the compound interest by subtracting the principal amount from the future value:

Compound Interest = A - P
Compound Interest = K510.05 - K500
Compound Interest = K10.05

Therefore, the compound interest earned on an investment of K500 at 2% p.a. compounded half-yearly for one year is K10.05.

$$ A = P(1 + \frac{r}{100n})^{nt} $$

$$ A = 500(1 + \frac{2}{100 \times 2})^{2 \times 1} $$

$$ A = 500(1 + \frac{1}{50})^{2} $$

$$ A = 500(1.01)^{2} $$

$$ A = 500 \times 1.0201 $$

$$ A = 510.05 $$

Compound interest = A - P

$$ = 510.05 - 500 $$

$$ = 10.05 $$

Therefore, the compound interest is K10.05.