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(i) Find the population in 2001.

(ii) What would be its population in 2005?

Answer :

(i) We are given: Population in 2003 = 54,000, Rate = 5% p.a.

Time = 2003 – 2001 = 2 years

\(Population\; in \;2003 = Population\; in \;2001\times(1+\frac{R}{100})^n\)

\(\Rightarrow 54,000=Population\; of \;2001\times(1+\frac{5}{100})^2\)

\(\Rightarrow 54,000=Population \;of \;2001\times(\frac{21}{20})^2\)

\(\Rightarrow 54,000=Population\; of \;2001\times(\frac{441}{400})\)

∴ Population of 2001= \(\frac{54,000\times 400}{441}\)

= \(\frac{21,6,00,000}{441}=48,979.59≈48,980\)

(ii) \(Population \;in \;2005= Population\;in\;2003\times(1+\frac{R}{100})^n\)

\( =54,000\times(1+\frac{5}{100})^2\)

\( =54,000\times(\frac{21}{20})^2\)

\( =54,000\times(\frac{441}{400})^2\)

\(=135\times441=59,535\)

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- 2.Kamala borrowed ₹ 26,400 from a Bank to buy a scooter at a rate of 15% per annum compounded yearly. What amount will she pay at the end of 2 years and 4 months to clear the loan? (Hint: Find amount for 2 years with interest is compounded yearly and then find SI on the 2nd year amount for \(\frac { 4 }{ 12 }\) years).
- 3. Fabina borrows Rs 12,500 at 12% per annum for 3 years at simple interest and Radha borrows the same amount for the same time period at 10% per annum, compounded annually. Who pays more interest and by how much?
- I borrowed ₹ 12,000 from Jamshed at 6% per annum simple interest for 2 years. Had I borrowed this sum at 6% per annum compound interest, what extra amount would I have to pay?
- 5.Vasudevan invested ₹ 60,000 at an interest rate of 12% per annum compounded half yearly. What amount would he get (i) after 6 months? (ii) after 1 year?
- 6. Arif took a loan of ₹ 80,000 from a bank. If the rate of interest is 10% per annum, find the difference in amounts he would be paying after \(1\frac { 1 }{ 2 }\) years if the interest is (i) compounded annually. (ii) compounded half yearly.
- 7.Maria invested ₹ 8,000 in a business. She would be paid interest at 5% per annum compounded annually. Find (i) The amount credited against her name at the end of the second year. (ii) The interest for the third year.
- 8. Find the amount and the compound interest on ₹ 10,000 for \(1\frac { 1 }{ 2 }\) years at 10% per annum, compounded half yearly. Would this interest be more than the interest he would get if it was compounded annually?
- 9. Find the amount which Ram will get on ₹ 4,096, if he gave it for 18 months at \(12\frac { 1 }{ 2 }\) per annum, interest being compounded half yearly.
- 11. In a Laboratory, the count of bacteria in a certain experiment was increasing at the rate of 2.5% per hour. Find the bacteria at the end of 2 hours if the count was initially 5,06,000.
- 12.A scooter was bought at ₹ 42,000. Its value depreciated at the rate of 8% per annum. Find its value after one year.

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