$A$ man borrows ₹ $4000$ from a bank at $7 \frac{1}{2} \%$ compound interest. At the end of every year,he pays ₹ $1500$ as part repayment of the loan and interest. How much does he still owe to the bank after three such instalments (in ₹)?

The population of a state increases by $10 \%$ every year. If its population in the year $2003$ was $15$ lakhs,what was its population in the year $2005$ (in lakhs)?

Which information given below is sufficient to know the principal amount if the difference between the $C.I.$ and $S.I.$ for $2$ years is $18$?
$(I)$ The rate is same at which an amount of $Rs. 1000$ becomes $1120$ in $2$ years under $S.I.$
$(II)$ The principal is $Rs. 2000$.

On what sum will the compound interest (in ₹) for $2 \frac{1}{2}$ years at $10 \%$ per annum amount to ₹ $6352.50$?

Mr. Dua invested money in two schemes $A$ and $B$ offering compound interest at $8 \%$ per annum and $9 \%$ per annum respectively. If the total amount of interest accrued through two schemes together in two years was ₹ $4818.30$ and the total amount invested was ₹ $27000$. What was the amount (in ₹) invested in scheme $A$?

The compound interest earned by Shivam on a certain amount at the end of $2$ years at the rate of $8 \, p.c.p.a.$ was $Rs. 1414.4$. What was the total amount that Shivam got back at the end of $2$ years in the form of principal plus interest earned (in $Rs.$) (in $.4$)?