**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 % 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 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

**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 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.

**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?

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.

**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? (**Hint:** Find A for 2 years with interest is compounded yearly and then find SI on the 2nd year amount for 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.

**1 **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 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 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 -...

**1 ** Calculate the amount and compound interest on

(a) Rs 10,800 for 3 years at % 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.

- Previous
- Next

Exams

Articles

Questions