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Directions: Read the followin questions carefully and answer them:
1
Find compound interest on Rs. 7000 at 21% per annum for 2 years 4 months, compounded annually.
» Explain it
B
Time = 2 years 4 months = 2 4  years  = 2 1  years.
12 3

Let principal = P, Rate = R% per annum, Time = n years.

When interest is compounded annually. then,

Amount  =  P ( 1 +  R ) n
100  

So, amount = Rs [ 7000 ×  ( 1 +  21 ) 2 ]  ×  ( 1 +   1/3 × 21 )]
100   100

⇒  Rs. ( 7000 ×   121   ×   121  ×  107 )
100 100 100

⇒  10966.1.

So, C.I. = Rs. (10966.1 – 7000)  ⇒  Rs. 3966.1.

Hence, option B is correct.

2
Find the compound interest on Rs. 7500 in 2 years at 6% per annum, the interest being compounded half-yearly.
» Explain it
A
When interest is compounded Half-yearly. then,

Amount = P [ 1 +  (R/2) ] 2T
100  

Principal  = Rs. 7500; Rate = 3% per half - year; Time = 2 years = 4 half - years.

So, Amount = Rs.  [ 7500 ×  ( 1 +  3 ) 4 ]
100  

⇒   Rs. ( 7500  ×  103  ×  103  ×  103  ×  103 )
100 100 100 100

⇒  Rs. 8441.31

⇒ C.I = Rs. (8441.31 - 7500)  = Rs. 941.31.

Hence, option A is correct.

3
Find the compound interest on Rs. 10,000 at 20% per annum for 6 months. compounded quarterly.
» Explain it
C
P = 10000, T = 6 months, R = 20/4 = 5%   (rate of interest apply quaterly)


By the net% effect we would calculate the effective compound rate of interest for 6 months = 10.25%  (Refer to sub-details)

CI = 10.25% of 10000

CI =   10.25 × 10000  = 1025.
100
_________________________________________________________________

Sub-details:

Calculation of effective compound rate of interest for 2 quaters (6 months) will be as follows.

Here, x = 5 and y = 5%


Net% effect = x + y =  xy  
100

= 5 + 5 +  5 × 5  = 10 + 0.25 = 10.25%
100

_______________________________________________________

Traditional Method:

When interest is compounded Quarterly. then,

Amount = P [ 1 + (R/4) ] 4T
100  

Principal = Rs. 10000; Time = 6 months = 2 quarters; Rate = 20% per annum = 5% per quarter

So, Amount = Rs [ 10000 ×  ( 1 +  5 ) 2 ]
100  

⇒  Rs ( 10000 ×  21   ×  21 )   ⇒ 11025.
20 20

So, C.I = Rs (11025 – 10000) ⇒  Rs 1025.

Hence, option C is correct. 

4
If the simple interest on a sum of money at 5% per annum for 2 years is Rs. 1400, find the compound interest on the same sum for the same period at the same rate.
» Explain it
B
We know, that

SI = rt%  (rate of interest & time)  and  by the net% effect we would calculate the effective compound rate of interest for 2 years = 10.25% (Refer to sub-details)

1400 = (2 × 5)%

So, 10% ≡ ₹ 1400

10.25% ≡ ₹ x

By the cross multiplication, we get

x =  1400 × 10.25  = ₹ 1435.
10
_______________________________________________________________________

Sub-details:


Calculation of effective compound rate of interest for 2 years will be as follows.

Here, x = 5 and y = 5%

 
Net% effect = x + y =  xy  
100

= 5 + 5 +  5 × 5  = 10 + .25 = 10.25%
100

_______________________________________________________________________

Traditional Method:

Clearly, Rate = 5% p.a, Time = 2 years, S.I = Rs. 1400.

So, principal = Rs. ( 100 × 1400 ) = Rs. 14000.
2 × 5

Amount = Rs. [ 14000 ×  ( 1 +  5 ) 2 ]   ⇔ Rs. ( 14000 ×  21  ×  21 )  ⇒ Rs. 15435.
100   20 20

So, C.I = Rs. (15435 – 14000) = Rs. 1435.

Hence, option B is correct.

5
If Rs. 1000 amounts to Rs. 1166.40 in two years compounded annually, Find the rate of interest per annum.
» Explain it
D
Principal = Rs. 500; Amount = Rs. 583.20; Time = 2 years.
Let the rate be R% per annum. then,

[ 1000 ( 1 +  R ) 2 ]  = 1166.40.
100  
                    Or
( 1 +  R ) 2  =  ( 108 ) 2
100   100  

⇒ 1 +  R   =   108   or  R = 8.
100 100

So, Rate = 8% p.a

Hence, option D is corret.