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

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)

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)

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)

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.

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.

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 =
...

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

(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...

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.

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.

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.

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.

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...

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.

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

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

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 -...

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

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

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