The effective annual rate of interest (in $\%$) corresponding to a nominal rate of $13 \%$ per annum payable half-yearly is:

At what rate per cent per annum will the simple interest on a sum of money be $\frac{2}{5}$ of the principal in $10$ $years$?

Brinda borrowed ₹ $1000$ to build a hut. She pays $5 \%$ simple interest. She lets the hut to Ramu and receives a rent of ₹ $12 \frac{1}{2}$ per month from Ramu. In how many years would Brinda clear off the debt?

In how many years will ₹ $150$ produce the same interest at $8 \%$ per annum as ₹ $800$ produces in $3$ years at $4 \frac{1}{2} \%$ per annum?

The population of Mumbai increases by $5 \%$ per annum. Its population was $100000$ in $2004$. What was its population after $3$ years?

Ram divided $2189$ into three parts such that the simple interest on them after $1, 2,$ and $3$ years respectively is equal. The rate of simple interest is $4\%$ per annum in all cases. The smallest part is (in $Rs.$):