## Results

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### #1. Find the simple interest on Rs. 5200 for 2 years at 6% per annum.

Solution:
P = Principal Amount
T = Time period
R = Rate of Interest
I = P×T×R/100
I = 5200×2×6/100
I = 624.

### #2. Rs. 1200 is lent out at 5% per annum simple interest for 3 years. Find the amount after 3 years.

Solution:
A = P I
A =1200 (PTR / 100)
A = [1200 (1200×5×3 / 100)]
Amount,
A = Rs.1380

### #3. Interest obtained on a sum of Rs. 5000 for 3 years is Rs. 1500. Find the rate percent.

Solution:
Let rate is R%
We have,
I=PTR/100
Here,
1500=5000×3×R/100
Thus,
R=10%

### #4. Rs. 2100 is lent at compound interest of 5% per annum for 2 years. Find the amount after two years.

Solution:
We can use formula of compound interest A=P×[1 (r/100)]n
A=2100×[1 (5100)]/2
A=2100×[105/100]/2
A=(2100×11025)/10000
Hence,
Amount
A=Rs.2315.25

### #5. Find the difference between the simple interest and the compound interest at 5% per annum for 2 years on principal of Rs. 2000.

Solution:
The difference between compound interest and simple interest over two years is given by
Pr2/1002 or P(r/100)2

Here, Principal(P)=Rs.2000

Rate(r)=5%

Now difference,

D=(2000×5×5)/(100×100)

D=Rs.5

### #6. Find the rate of interest if the amount after 2 years of simple interest on a capital of Rs. 1200 is Rs. 1440.

Solution:
Amount, A=Rs.1440
Principal, P=Rs.1200
Interest, I=Rs.(14401200)=240
R=(240×100)/(1200×2)=10%
Alternatively,We can go through athought process i.e.
1200==20%(240 in 2 years)1400
That means 10% rise in each year

### #7. What is the difference between the simple interest on a principal of Rs. 500 being calculated at 5% per annum for 3 years and 4% per annum for 4 years?

Solution:
I1=PT1R1/100
I1=(500×3×5)/100=Rs.75
I2=PT2R2/100
I2=(500×4×4)/100=Rs.80
Difference=8075=Rs.5

Alternatively
The interest is calculated simply and then it will have a rise of 15% in 1st case and 16% in 2nd case.
Difference = 1% on 500 = Rs. 5

Otherway,
500 == 15% ⇒ 575 (1st case)
500 == 16% ⇒ 580 (2nd case)
We can see clear difference of Rs. 5

### #8. What is the simple interest on a sum of Rs. 700 if the rate of interest for the first 3 years is 8% per annum and for the last 2 years is 7.5% per annum?

Solution:
1stcase:
I1=700×3×8/100=Rs168
2ndcase:
I2=700×2×7.5/100=Rs105

Then total interest for five years

=(I1 I2)=Rs273

Alternatively,
As interest is calculated as simple interest
So, we can add up rates for all given 5 years and calculate it easily i.e.
For the five years rate
= (8 × 3 7.5 × 2)
= 39%
Now,
700 = 39% ⇒ 973
Interest = Rs. 273
The thought can go this way we internally calculated

10% of 700=(700/10)=70
Then,
39% of 700=(40%1%) of 700
=(2807)
=273

### #9. Find the compound interest on Rs. 1000 at the rate of 20% per annum for 18 month when interest is compounded half yearly.

Solution:
Given,
Principal, P=Rs.1000
Compound rate, R=20% per annum
=20/2=10% half – yearly
Time=18 month= 3 half – years
Amount, A={P×[1 (R/100)]n}={1000×[1 (10/100)]3}
={(1000×11×11×11/10×10×10)}
A=Rs.1331
Hence, compound interest=Rs.331