Important for :
1
Akanskha invests Rs. x in insurance which gives her returns at 21% annually and Rs. y in mutual funds which gives her returns of 10% compounded half yearly. If Akanskha gets the same returns from both the investments after 1 year, then what is the square root of the ratio of x to y?
» Explain it
C
Amount earned from insurance after one year;

A1 = (100 + Interest) × Principal = 121% of x

Applying net% effect in the 2nd scenario to get the effective rate of interest compound half-yearly, we get

 Net% effect = x + y + xy % 100

Here, a = b = 5%
 = 5 + 5 + 5 × 5 = 10.25% 100

∴    Amount earned from mutual funds

A2 = (100 + interest) × Principal = (100 + 10.25)% = 110.25% of y

Given, A1 = A2

121% of x = 110.25% of y

 ∴ x = 110.25 = 441 y 121 484

∴
 x y
=
 441 484
= 21 : 22.

Hence, option C is correct.

2
Irfan borrows a sum of Rs. 64000 at 5% pa compound interest. He repays a certain amount at the end of one year and the balance amount of Rs. 35700 at the end of the second year. What amount does he repay in the first year?
» Explain it
E
Sum = Rs. 64,000

 ∴  CI for 1st year = 64,000 × 5 = Rs 3200 100

∴  A = 64,000 + 3200 = Rs. 67,200

let the amount repaid be Rs. x

Then, the sum at the beginning of the 2nd year = 67,200 – x

⇒ 35,700 = 1.05 × (67200 – x) × 1

⇒ x = Rs. 33,200.

Hence, option E is correct.

3
If the compound interest accrued on an amount of Rs. 15,000 in two years is Rs. 2,496, what is the rate of interest p.c.p.a.?
» Explain it
A
Principal (P) = Rs. 15000; CI = Rs. 2496; Time (t) = 2 years.

Let the rate be R% per annum. then,

 CI = [ P ( 1 + R ) t – 1 ] 100
Or
 ⇒   2496 = 15000 [( 1 + R ) 2 – 1 ] 100

⇒   2496  + 1 =  ( 1 +  R ) 2
 ⇒ 17496 = ( 1 + R ) 2 15000 100
15000 100

 ⇒ 729 = ( 1 + R ) 2 625 100

By comparing,

 ⇒ ( 27 ) 2 = ( 1 + R ) 2 ⇒ 27 = 1 + R 25 100 25 100

 ⇒ R = ( 27 – 1 ) × 100 ⇒ R = 8% 25

Hence, optinon A is correct.

4
What is be the compound interest (in Rs.) accrued on an amount of Rs. 15000 at the rate of 20 per cent annum in two years, if the interest is compounded half-yearly?
» Explain it
D
Rate of interest (half yearly) = 20/2 = 10%

Now, P = 15000, T = 2 = 4 half years

By the net% effect we would calculate the effective compound rate of interest for 4 half years = 46.41% (Refer to sub-details)

Therefore, CI = 46.41% of 15000

 CI = 46.41 × 15000 = ₹ 6961.5 100
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Sub-details:

Calculation of effective compound rate of interest for 4 half years will be as follows.

For the first 2 half years, let's apply the net% effect.

Here, x = y = 10%

 Net% effect = x + y = xy 100

 = 10 + 10 + 10 × 10 = 21% 100

Now let's take this 21% as x and 10% as y for the calculation of 3rd half year.

 = 21 + 10 + 21 × 10 = 33.1% 100

Similarly, let's take this 33.1% as x and 10% as y for the calculation of 4th half year.

 = 33.1 + 10 + 33.1 × 10 = 43.1 + 3.31 = 46.41% 100

_____________________________________________________________________

If interest is compounded half-yearly then time (t) = 2 × 2 = 4; r% = 20/2 = 10%

 A  = [ P ( 1 + R ) t 100
Or
 = 15000 [( 1 + 10 ) 4 100

 = 15000 × 11 × 11 × 11 × 11 = ₹ 21961.5 10 10 10 10

∴     CI = 21961.5 – 15000 = ₹ 6961.5

Hence, optiion D is correct.

5
The compound interest on Rs. 10,000 in 2 years at 4% per annum, the interest being compounded yearly, is
» Explain it
B
Rate of interest = 4%

Therefore, applying the net% effect formula for effective rate of compound interest for 2 years , we get

 Net% effect = x + y + xy % 100

x = y = 4%

 = 4 + 4 + 4 × 4 = 8 + .16 = 8.16% 100

CI = 8.16% of 10,000

 = 8.16 × 10000 = ₹ 816 100

Hence, option B is correct,