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Page No 65:
Question 1:
Mahadevan took out a loan of 5,000 rupees from a tank, which charges compound interest. The rate of interest was 10% for the first year, but it was increased to 12% during the second year. How much money should Mahadevan pay at the end of two years to settle the debt?
Answer:
Principal, P = Rs.5000
Rate of interest for the first year, R1= 10%
Rate of interest for the second year, R2= 12%
Total amount including interest = 
∴ Total amount including interest for the first year
Now, principal for the second year = Rs.5500
Total amount including interest for the second year
∴ Total amount to be paid by Mahadevan at the end of two years to settle the debt = Rs.6160
Page No 65:
Question 2:
Compute the compound interest for 25,000 rupees at 9% for 2 years.
Answer:
Principal, P = Rs.25000
Rate of interest, R = 9%
Time, n = 2 years
Total amount including interest =
∴ Total amount including interest
Compound interest = Amount − Principal
= Rs.29702.50 − Rs.25000
= Rs.4702.5
Page No 65:
Question 3:
Verghese borrowed 16,000 rupees from a bank at 8% compound interest. After 2 years, the interest rate was lowered to 6%. What is the total amount that Verghese has to repay at the end of 3 years?
Answer:
Principal, P = Rs.16000
Rate of interest for the first two years, R1 = 8%
Rate of interest for the third year, R2 = 6%
Total amount including interest =
∴ Total amount including interest for the first two years
Now, principal for the third year = Rs.18662.40
Total amount including interest
∴Amount to be repaid by Verghese at the end of 3 years = Rs.19782.14
Page No 67:
Question 1:
Rahim, Johny and Gopu deposited 10,000 rupees each, under different schemes, in a bank which gives 8% interest. Rahim gets simple interest, Johny gets interest compounded half-yearly and Gopu gets interest compounded quarterly. Compute the total amount each of them gets back after one year and compare these amounts.
Answer:
Amount deposited by Rahim, Johny and Gopu, P = Rs.10000
Rate of interest, R = 8%
Time, T = 1 year
For Rahim:
Simple interest =
Amount that Rahim gets = Principal + Simple interest
= Rs.10000 + Rs.800
= Rs.10800
For Johny:
Interest for the first half-year = Rs
= Rs.400
Principal for the second half-year = Principal + Interest
= Rs.10000 + Rs.400
= Rs.10400
Interest for the second half-year = Rs
= Rs.416
Amount Johny gets = Rs.10400 + Rs.416
= Rs.10816
For Gopu:
Interest for the first quarter = Rs
= Rs.200
Principal for the second quarter = Principal + Interest
= Rs.10000 + Rs.200
= Rs.10200
Interest for the second quarter = Rs
= Rs.204
Principal for the third quarter = Rs.10200 + Rs.204
= Rs.10404
Interest for the third quarter = Rs
= Rs 208.08
Principal for the fourth quarter = Rs.10404 + Rs.208.08
= Rs.10612.08
Interest for the fourth quarter = Rs
= Rs.212.24
Amount that Gopu gets = Rs.10612.08 + Rs.212.24
= Rs.10824.32
It can be observed that:
Amount received by Gopu > Amount received by Johny > Amount received by Rahim
Page No 67:
Question 2:
A person deposited 20,000 rupees in a bank which gives 6% interest compounded half-yearly. How much would he get back after 2 years?
Answer:
Amount deposited by the person, P = Rs.20000
Rate of interest, R = 6% compounded half-yearly
Time, T = 2 years
Simple interest is given by the formula
Interest for the first half of the first year = Rs
= Rs.600
Principal for the second half of the first year = Principal + Interest
= Rs.20000 + Rs.600
= Rs.20600
Interest for the second half of the first year = Rs
= Rs.618
Principal for the first half of the second year = Rs.20600 + Rs.618
= Rs.21218
Interest for the first half of the second year = Rs
= Rs.636.54
Principal for the second half of the second year = Rs.21218 + Rs.636.54
= Rs.21854.54
Interest for the second half of the second year = Rs
= Rs.655.64
∴Amount received by the person after two years = Rs.21854.54 + Rs.655.64
= Rs.22510.18
Page No 67:
Question 3:
Ravi deposited 50,000 rupees in a bank, which gives 6% interest, compounded quarterly. How much would he get back after 9 months?
Answer:
Amount deposited by Ravi, P = Rs.50000
Rate of interest, R = 6% compounded quarterly
Time, T = 9 months = 3 quarters
Simple interest is given by the formula
Interest for the first quarter = Rs
= Rs.750
Principal for the second quarter = Rs.50000 + Rs.750
= Rs.50750
Interest for the second quarter = Rs
= Rs.761.25
Principal for the third quarter = Rs.50750 + Rs.761.25
= Rs.51511.25
Interest for the third quarter = Rs
= Rs.772.67
∴ Amount received by Ravi after nine months = Rs.51511.25 + Rs.772.67
= Rs.52283.92
Page No 67:
Question 4:
Lathika deposited 25,000 rupees in a bank which gives 8% interest compounded half-yearly. Najma deposited the same amount at the same rate of interest, but compounded quarterly. What is the difference in the amounts they would get back after one year?
Answer:
Amount deposited, P = Rs.25000
Rate of interest = 8% compounded half-yearly
Time, T = 1 year
For Lathika:
Simple interest is given by the formula
Interest for the first half of the first year = Rs
= Rs.1000
Principal for the second half of the first year = Principal + Interest
= Rs.25000 + Rs.1000
= Rs.26000
Interest for the second half of the first year = Rs
= Rs.1040
Amount received by Lathika after one year = Rs.26000 + Rs.1040
= Rs.27040
For Najma:
Interest for the first quarter = Rs
= Rs.500
Principal for the second quarter = Principal + Interest
= Rs.25000 + Rs.500
= Rs.25500
Interest for the second quarter = Rs
= Rs.510
Principal for the third quarter = Rs.25500 + Rs.510
= Rs.26010
Interest for the third quarter = Rs
= Rs.520.20
Principal for the fourth quarter = Rs.26010 + Rs.520.20
= Rs.26530.20
Interest for the fourth quarter = Rs
= Rs.530.60
Amount Lathika get back after one year = Rs.26530.20 + Rs.530.60
= Rs.27060.80
Difference between their amounts = Rs.27060.80 − Rs.27040
= Rs.20.80
Page No 68:
Question 1:
A man deposits 50,000 rupees in a financial company, which gives 9% interest compounded every three months. How much would he get back after one year?
Answer:
Amount deposited by the man, P = Rs.50000
Rate of interest, R = 9%
Time, T = 1 year
Simple interest is given by the formula
The interest is compounded quarterly
∴ Interest for the first quarter = Rs
= Rs.1125
Principal for the second quarter = Rs.50000 + Rs.1125
= Rs.51125
Interest for the second quarter = Rs
= Rs.1150.31
Principal for the third quarter = Rs.51125 + Rs.1150.31
= Rs.52275.31
Interest for the third quarter = Rs
= Rs.1176.19
Principal for the fourth quarter = Rs.52275.31 + Rs.1176.19
= Rs.53451.50
Interest for the fourth quarter = Rs
= Rs.1202.66
∴Amount received by the man after one year = Rs.53451.50 + Rs.1202.66
= Rs.54654.16
Page No 69:
Question 1:
The population of Kerala increases by 2% every year. The current population is 3 crores. What would be the population after 3 years?
Answer:
Current population of Kerala, P = 30000000
Rate of increase, r = 2%
Time, n = 3 years
Population after n years can be calculated using the formula
∴ Population after 3 years
Page No 69:
Question 2:
A TV manufacture reduces the price of a particular model by 5% every year. The current price of this model is 8000 rupees. What would be the price after 3 years?
Answer:
Current price of TV, P = Rs.8000
Rate of reduction, r = 5%
Time, n = 3 years
Price of TV after n years can be calculated using the formula
∴ Price of TV after 3 years
Page No 69:
Question 3:
Abu, Babu and Sabu deposited 10000 rupees each, under various schemes which give 10% interest. Abu gets interest compounded annually, Babu gets interest compounded every half-year and Sabu gets interest compound every quarter. Compute the total amount each would get after 2 years.
Answer:
Money deposited by Abu, Babu and Sabu, P = Rs.10000
Rate of interest, r = 10%
Time, n = 2 years
For Abu:
We know that A =
∴ Amount received by Abu after 2 years
For Babu:
Simple interest is given by the formula
Interest for the first half of the first year = Rs
= Rs.500
Principal for the second half of the first year = Principal + Interest
= Rs.10000 + Rs.500
= Rs.10500
Interest for the second half of the first year = Rs
= Rs.525
Principal for the first half of the second year = Rs.10500 + Rs.525
= Rs.11025
Interest for the first half of the second year = Rs
= Rs.551.25
Principal for the second half of the second year = Rs.11025 + Rs.551.25
= Rs.11576.25
Interest for the second half of the second year = Rs
= Rs.578.81
∴ Amount received by Babu after two years = Rs.11576.25 + Rs.578.81
= Rs.12155.06
For Sabu:
Interest for the first quarter of the first year = Rs
= Rs.250
Principal for the second quarter of the first year = Principal + Interest
= Rs.10000 + Rs.250
= Rs.10250
Interest for the second quarter of the first year = Rs
= Rs.256.25
Principal for the third quarter of the first year = Rs.10250 + Rs.256.25
= Rs.10506.25
Interest for the third quarter of the first year = Rs
= Rs.262.66
Principal for the fourth quarter of the first year = Rs.10506.25 + Rs.262.66
= Rs.10768.91
Interest for the fourth quarter of the first year = Rs
= Rs.269.22
Principal for the first quarter of the second year = Rs.10768.91 + Rs.269.22
= Rs.11038.13
Interest for the first quarter of the second year = Rs
= Rs.275.95
Principal for the second quarter of the second year = Rs.11038.13 + Rs.275.95
= Rs.11314.08
Interest for the second quarter of the second year = Rs
= Rs.282.85
Principal for the third quarter of the second year = Rs.11314.08 + Rs.282.85
= Rs.11596.93
Interest for the third quarter of the second year = Rs
= Rs.289.92
Principal for the fourth quarter of the second year = Rs.11596.93 + Rs.289.92
= Rs.11886.85
Interest for the fourth quarter of the second year = Rs
= Rs.297.17
Amount received by Sabu after two years = Rs.11886.85 + Rs.297.17
= Rs.12184.02
Page No 69:
Question 4:
A financial company claims that it charges only 20% interest on loans. But if a person takes out a loan of 100 rupees, he would get only 80 rupees, after subtracting the annual interest of 20 rupees at the outset. And he has to pay back 100 rupees after one year. What is their actual rate of interest?
Answer:
If a person takes a loan of Rs.100, the financial company would give him Rs.80 after subtracting the interest of Rs.20.
Principal, P = Rs.80
Let the actual rate of interest be r%.
Amount after n years can be calculated using the formula
Amount after an year = Rs.100
Thus, the actual rate of interest is 25%.
Page No 69:
Question 5:
Dileep and Manoj deposited the same amount under different schemes giving 10% interest. Dileep gets only simple interest, while Manoj gets interest compounded annually. After 2 years, Manoj had 50 rupees more than Dileep. How much money did each deposit?
Answer:
Rate of interest for Dileep and Manoj, R = 10%
Time, T = 2 years
Let the money each deposited be P.
For Dileep:
Simple interest =
Amount received by Dileep = Principal + Simple interest
= P +
For Manoj:
Amount =
Amount received by Manoj = Rs.50 + Amount received by Dileep
Thus, Dileep and Manoj deposited Rs.5000.
Page No 70:
Question 1:
A person deposits 6400 rupees in a bank, which gives 12% interest. How much interest would he get after one month? What would be the interest for one month at 6%? What if it is 3%?
Answer:
Principal, P = Rs.6400
Rate of interest, R1 = 12%
Time, T = 1 month
Simple interest is given by the formula
Interest for the first month = Rs
= Rs.64
Rate of interest, R2 = 6%
Interest for the first month = Rs
= Rs.32
Rate of interest, R3 = 3%
Interest for the first month = Rs
= Rs.16
∴ Interest for one month at 12% = Rs.64
Interest for one month at 6% = Rs.32
Interest for one month at 3% = Rs.16
Page No 70:
Question 2:
What is the interest for 16,000 rupees at for one year? What would be the interest if the rate of interest is only.
Answer:
Principal, P = Rs.16000
Rate of interest, R1 = %
Time, T = 1 year
Simple interest =
Rate of interest, R2 = %
Simple interest
= Rs.1000
∴ Interest for one year at % = Rs.2000
Interest for one month at % = Rs.1000
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