Relationship between annual nominal rate of interest and annual effective rate of interest, if frequency of compounding is greater than one

A sum of money invested in compounded interest doubles itself in four years. In how many years it becomes 32 times of itself as the same rate of compound interest?

The simple interest on $\displaystyle 600$ for 9 months is $\displaystyle 27$. Find the interest rate.

Miss Liza lent $\displaystyle 4,000$ in such a way that some amount was given to Mr. A at $\displaystyle 3\%$ p.a. S.I. and rest amount to was given to B at $\displaystyle 5\%$ p.a. S.I., the annual interest from both is $\displaystyle 144$. Find the amount lent to Mr. A.

A certain sum of money was put at S.I. for $\displaystyle 2.5$ years at a certain rate of S.I. p.a. Had it been put at $\displaystyle 4\%$ higher rate, it would have fetched $\displaystyle 500$ more. Find the sum of money.

Rs.$\displaystyle 1,25,000$ is borrowed at compound interest at the rate of $\displaystyle 2\%$ for the 1st year, $\displaystyle 3\%$ for the second year and $\displaystyle 4\%$ for the 3rd year. Find the amount to be paid after 3 years.

If $\displaystyle \text{Rs. }1,000$ be invested at interest rate of $\displaystyle 5\%$ and the interest be added to the principal every $\displaystyle 10$ years, then the number in years in which it will amount to $\displaystyle \text{Rs. }2,000$ is: