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Answer :

We have: Initial count of bacteria = 5,06,000

Rate = 2.5% per hour

n = 2 hours

So, we have:

num. of bacteria(end of 2 hours)=Num. of count of bacteria initially\(\times(1+\frac{R}{100})^n\)

\( =5,06,000\times(1+\frac{2.5}{100})^2\)

\( =5,06,000\times(\frac{41}{40})^2\)

\( =5,06,000\times(\frac{1681}{1600})^2\)

\( =5,31,616.25\)

Hence we have, the number of bacteria after two hours = 5,31,616

(approx).

- 1. Calculate the amount and compound interest on (a)₹ 10,800 for 3 years at \(12\frac { 1 }{ 2 }\) % per annum compounded annually. (b)₹ 18,000 for \(2\frac { 1 }{ 2 }\) years at 10% per annum compounded annually. (c)₹ 62,500 for \(1\frac { 1 }{ 2 }\) years at 8% per annum compounded half yearly. (d) ₹ 8,000 for 1 year at 9% per annum compounded half yearly. (You could use the year by year calculation using SI formula to verify). (e)₹ 10,000 for 1 year at 8% per annum compounded half yearly.
- 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.
- 10.The population of a place increased to 54,000 in 2003 at a rate of 5% per annum. (i) Find the population in 2001. (ii) What would be its population in 2005?
- 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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