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12   A scooter was bought at Rs 42,000. Its value depreciated at the rate of 8% per annum. Find its value after one year.
 

Given, Principal = Rs 42,000 Rate of depreciation = 8% p.a  Reduction = 8% of Rs 42000 per year                  Value at the end of 1 year = Rs (42000 – 3360) = Rs 38,640

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. 

Given, Initial count of bacteria, P = 5, 06,000 (Principal Amount) Rate of increase, R = 2.5% per hour. Time period, n = 2 hours (This question is done in a similar manner as compound interest) Number of bacteria after 2 hours =  Therefore, the number of bacteria at the end of 2 hours will be 531616 (approx)  

10   The population of a place increased to 54,000 in 2003 at a rate of 5% per annum.

                   (ii) what would be its population in 2005?

Let the population in 2001 be P'  Compound rate of increase = 5% p.a. The population in 2005 will be more than in 2003 Time period, n = 2 years    (2003 to 2005)   Therefore, the population in 2005 will be 59535 (approx)

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.

Let the population in 2001 be P  Compound rate of increase = 5% p.a. The population in 2003 will be more than in 2001 Time period, n = 2 years    (2001 to 2003)   Therefore, the population in 2001 was 48980 (approx)  

9  Find the amount which Ram will get on Rs 4,096 if he gave it for 18 months at  12\frac{1}{2} % per annum, interest being compounded half-yearly. 

Given, Principal amount, P = Rs 4,096 Rate of interest, R   Time period, n = 18 months = (12 + 6) months = 1.5 years = 3 half years (There are 3 half years in 1.5 years) We know,  Amount when interest is compounded annually, (A)    Therefore, the required amount                   Ram will get Rs 4,913 after 18 months.  

]7    Maria invested Rs 8,000 in a business. She would be paid interest at 5% per annum compounded annually. Find

          (ii) The interest for the 3rd year.

Now, The amount after 2nd year will become the principal amount for the 3rd year Principal amount, P = Rs 8,820 Compound rate of interest, R = 5% p.a. Time period, n' = 1 year   Therefore, the interest for the 3rd year is Rs 441.

8.  Find the amount and the compound interest on Rs 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?
 

Principal = Rs.10,000 Time =      years Rate = 10% per annum CASE 1  Interest on compounded half yearly. Rate = 10% per annum  = 5 % per half yearly     = Amount CI = Amount - principal CI  =  CI = 1576.25 CASE 2     Interest on compounded anually Rate = 10% per annum  = Amount CI = Amount - principal CI  =  CI = 1000   Interest for half years on 11000 =  = 550 Total interest =     ...

 7  Maria invested Rs 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.
 

Given, Principal amount, P = Rs 8,000 Compound rate of interest, R = 5% p.a. Time period, n = 2 years We know, Amount when interest is compounded annually, A =                                                                    Therefore, the amount credited against her name at the end of the second year is Rs 8,820  

 Arif took a loan of Rs 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.

(i) Given, Principal amount, P = Rs 80000 Rate of interest, R = 10% p.a. Time period =  years. We know, Amount when interest is compounded annually, A = Now, For the first year, A=           For the next half year, this will act as the principal amount.  Interest for 1/2 year at 10% p.a =                  Required total amount = Rs (88000 + 4400) = Rs 92400 (ii) If it is compounded half...

5  Vasudevan invested Rs 60,000 at an interest rate of 12% per annum compounded half yearly. What amount would he get

                   (ii) after 1 year? 

Given, Principal, P = Rs 60,000 Compound interest rate, R = 12% p.a                                             = 6 % half yearly For a period of 1 year.  Time period, n = 2 half years (As there are 2 half years in a year.) We know, Amount when interest is compounded annually, A =    After 1 year, Vasudevan would get an amount Rs. 67416.

5  Vasudevan invested Rs 60,000 at an interest rate of 12% per annum compounded half yearly. What amount would he get

                 (i) after 6 months? 

Given, Principal, P = Rs 60,000 Compound interest rate, R = 12% p.a                                             = 6 % half yearly For a period of 6 months.  Time period, n = 1 half year (As there is 1 half year in 6 months.) We know, Amount when interest is compounded annually, A =                     After 6 months, Vasudevan would get an amount Rs. 63600.  

4. I borrowed Rs 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? 

Given, Principal,P =Rs 12000  Simple interest Rate,R = 6% p.a. Time period,n = 2 years.   Simple Interest, SI at 6% for 2 years =              If he would have borrowed it at a compound interest Rate, R = 6% p.a. We know, Amount when interest is compounded annually, A =      He would have to pay Rs (1483.20 - 1440) = Rs 43.20 extra.

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? 

For Fabina, Principal,P =Rs 12500  Simple interest Rate,R = 12% p.a. Time period,n = 3 years.   Simple Interest, SI at 12% for 3 years =  = Rs 4500 For Radha, Principal,P =Rs 12500  Compound interest Rate,R = 10% p.a. Time period,n = 3 years.  We know, Amount when interest is compounded annually,    Fabina pays more interest and Rs (4500 - 4137.50) = Rs 362.50 more.

Kamala borrowed Rs 26,400 from a Bank to buy a scooter at a rate of 15% p.a. compounded yearly. What amount will she pay at the end of 2 years and 4 months to clear the loan? (Hint: Find A for 2 years with interest is compounded yearly and then find SI on the 2nd year amount for  \frac{4}{12}  years )

The amount borrowed from the bank = Principal amount, P = Rs 26400 Compound interest rate, R = 15% p.a. Time period = 2 years 4 months =  We know, Amount when interest is compounded annually, A = Therefore, for the first 2 years, amount, A =  = Rs 34914 Now, this would act as principal for the next 1/3 year. We find the SI on Rs 34914 for 1/3 year. SI =  = Rs 1745.70 Therefore, Required...

1    Calculate the amount and compound interest on

        (e)  Rs 10,000 for 1 year at 8% per annum compounded half yearly.        

Given, Principal, P =Rs.10000,  Rate, R = 8% per annum compounded half yearly for 1 year.  Now, There are two half years in a year. Therefore compounding has to be 2 times.  And rate = half of 10% = 5% half yearly. Therefore, the required amount =   = Rs. 10816 And Compound Interest, C.I. = Amount - Principal = Rs. (10816 - 10000) = Rs. 816.

Calculate the amount and compound interest on:

(d) Rs 8000 for 1 year at 9% per annum compounded half yearly.   (You could use the year by year calculation using SI formula to verify)

Given, Principal,P =Rs.8000,  Rate, R =   9% per annum compounded half yearly for 1 year.  Now, There are two half years in a year. Therefore compounding has to be 2 times.  And rate = half of 9% = 4.5% half yearly. Therefore, the required amount =   = Rs. 8736.20 And Compound Interest, CI = Amount - Principal = Rs. (8736.20 - 8000) = Rs. 736.20  

Q : 1       Calculate the amount and compound interest on

             (c)   Rs 62,500 for   1\frac{1}{2}   years at 8% per annum compounded half yearly.
 

Given, Principal,P =Rs 62500,  Compound interest Rate,R = 8% compounded half yearly for 1.5 years. Since it is compounded half yearly, R becomes half = 4%, and time period doubles, n = 3 years. We know, Amount when interest is compounded annually, A = Therefore, the required amount =   = Rs.70304 And Compound Interest, CI = Amount - Principal = Rs. (70304 - 62500) = Rs. 7804

1    Calculate the amount and compound interest on 

            (b) Rs 18,000 for  2\frac{1}{2}   years at 10% per annum compounded annually.

Given, Principal,P =Rs.18000,  Rate,R = 10%   and time period,n = 2.5 years.  We know, Amount when interest is compounded annually = Amount after 2 years at 10% , A =  = Rs.21780 This acts as the principal amount for the next half year. SI on next 1/2 year at = = Rs. 1089 Therefore, Total amount to be paid after 2.5 years = Rs. (21780+1089) = Rs.22869 Now, Compound Interest after 2 years = A -...

     Calculate the amount and compound interest on


              (a)  Rs 10,800 for 3 years at  12\frac{1}{2} %  per annum compounded annually.

Given, Principal,P = Rs 10800   Compound Interese Rate,R =    p.a. Time period,n = 3 years.  We know, Amount when interest is compounded annually, A = Therefore, the required amount =   = Rs. 15377.34 And Compound Interest, CI = Amount - Principal = Rs. (15377.34 - 10800) = Rs. 4577.34

2    Find the population of a city after 2 years, which is at present 12 lakh, if the rate of increase is 4%.

Current population of city = 12 lakh 1200000  Population after two years =  Thus, the  population after two years is 1297920.
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