# Comparing Quantities

Exercise 3

1. Calculate the amount and compound interest on

(a) Rs 10,800 for 3 years at 12.5% per annum compounded annually. (b) Rs 18,000 for 2.5 years at 10% per annum compounded annually. (c) Rs 62,500 for 1.5 years at 8% per annum compounded half yearly. (d) Rs 8,000 for 1 year at 9% per annum compounded half yearly. (e) Rs 10,000 for 1 year at 8% per annum compounded half yearly. Alternate method:

Calculating big multiplication can be tedious. Compound interest can also be calculated by finding yearly amount for each year separately.

1st half year 10000+400=10400

2nd half year 10400+416=10816

2. 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?

Answer: Amount after 1st year 26400 + 3960 = 30360

Amount after 2nd year 30360 + 4554 = 34914

To make things easier interest can be bifurcated into two parts of 10% and 5% as follows:

1st year 26400 + 2640 + 1320 = 30360

2nd year 30360 + 3036 + 1518 = 34914 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? Interest paid by Fabina is Rs. 362.50 more than that paid by radha

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?

Answer: The extra amount payable would be interest on the first year’s interest

1st year’s interest = 12000 x 6%=720

Interest on 720 = 720 x 6%=43.20

Extra amount payable = Rs. 43.20

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?

Answer: Amount = 60000+60000 x 6%=60000+3600=63600

(ii) after 1 year?

Answer: Amount = 63600+63600 6% = 63600+3816=67416

6. 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 1.5 years if the interest is

(i) compounded annually.

=80000+80000 10%=80000+8000=88000

Interest for the next 6 months = 88000 x 5%=4400

Amount after 1.5 years = 88000+4400 = 92400

(ii) compounded half yearly.

Answer: rate of interest will become half and time will be three half years. 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. Interest after 2 years = 8820-8000=820

(ii) The interest for the 3rd year.

Interest for the 3rd year = 8820 x 5%=441

8. Find the amount and the compound interest on Rs 10,000 for 1.5 years at 10% per annum, compounded half yearly. Would this interest be more than the interest he would get if it was compounded annually? Interest = 11576.25-10000=1576.25

This interest would be more than the interest compounded annually, as interest compounded half yearly is always more than compounded annually at the same rate of interest.

9. Find the amount which Ram will get on Rs 4096, if he gave it for 18 months at 12.5% 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.

Answer: Let us assume the population to be P in 2001 which can be said to be 48980 in round figures.

(ii) what would be its population in 2005? 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.

Answer: The bacteria’s growth will be compounded after every hour which is 531616 in round figures

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.

Answer: Value of scooter after 1 year

= 42000-42000 x 8% = 42000-3360 = 38640

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