Compound Interest

The following question is followed by three statements numbered I, II and III. Read all the statements and answer accordingly.

What is the monthly income of Mr. X?

I. Mr. X spends $85\%$ of his income on various items and saves the remaining amount

II. Monthly saving of Mr. X is $₹4500$.

III. Out of the total money spent by Mr. X in a month, one-fifth is spent on food and remaining amount of $₹20400$ on other items.

Sneha opened a cumulative time deposit account with a bank and deposits $₹500$ for  $1\frac{1}{4}$ yr. If she receives$₹300$ as interest, then find the rate of interest per annum.

The annual rate of growth in population of a town is $10\%$. If its present population is $33275$, then the population of the town $3$ years ago was _____.

A man borrowed a sum of money at $5\%$ simple interest per annum and give the money to another person at $10\%$ compound interest and make a profit of $₹905$ in $3$ years. How much money in $₹$ did he borrow?

Mr. Sunil invested $₹3,00,000$ in shares two years ago. He incurred a loss of $5\%$ during the first year while earned a profit of $10\%$ on the balance amount during the second year. Calculate his net profit or loss after the second year.

The value of a machine depreciates at the rate of $10\%$ per annum. Mr Agarwal buys a machine for $₹5,00,000$ . In how many years will its value be reduced to $₹3,64,500$?

Three years ago, the population of a city was $50000$. If the annual increase during three successive years is $5\mathrm{\%}$, $8\mathrm{\%}$ and $10\mathrm{\%}$ respectively, find the present population of the city.

In a laboratory, the count of bacteria in a certain experiment was increasing at the rate of $2.5\mathrm{\%}$ per hour. Find the bacteria approximately at the end of $2$ hours if the count was initially $\mathrm{5,06,000}.$

The birth rate and death rate per year of a village are $6\%$ and $4\%,$ respectively. If the total population of the village is $40,000,$ find the population after two years.

The compound interest for two years on a capital is rupees two more than the simple interest for the same period. If the rate of interest is $5℅$ per year. Then the capital would be ₹$800$.

In compound interest, the principal remains constant for the whole period.

If the compound interest for $₹4000$ at the rate of $5\%$ for $2$ years is $₹k$, then find the value of $k$.

At same rate of simple interest, $A$ lent $₹6000$ to $B$ for $2$ years and $₹1500$ to $C$ for $4$ years and received $₹900$ as interest from both of them together. Find the rate of interest per annum.

A man invests $₹ 46875$ at $4\%$p.a. compound interest for $3$ years. Calculate the interest for the first year.

A sum is taken for one year at $16\%$ p.a. If interest is compounded after every three months, how many times will interest be charged in one year?( write the final answer in numerals)

Jacob deposited $₹9000$ in a bank which pays him $8\%$ interest per annum compounded quarterly. What is the amount which he received after $6$ months.

Find the amount he received on $₹3,20,000$ for one year at the rate of $20\%$ per annum if the interest rate is compounded quarterly.

Find the compound interest on $₹8000$ for $9$ months at $20\%$ per annum compounded quarterly.

Find the compound interest on $₹1,60,000$ for one year at the rate of $20\%$ per annum, if the interest is compounded quarterly.

If the amount when $₹1,25,000$ is invested for $9$ months at $8\%$ per annum, compounded quarterly is $₹ k$, find the value of $k$