PERCENT AND INTERESTS RELATED QUESTION

In this session, we will solve some percent and interests related GMAT question. If you have not gone through Percent and Interests section, I would recommend to first go through them and then proceed with this section.

 

GMAT Question –

Question 1 –

Leona bought a 1-year, $10,000 certificate of deposit that paid interest at an annual rate of 8 percent compounded semiannually. What was the total amount of interest paid on this certificate at maturity?

(A) $10,464
(B) $ 864
(C) $ 816
(D) $ 800
(E) $ 480

 

Method 1 –

Now, the question says that Leona brought a certificate of 10000 for 1-year with annual rate of 8 percent compounded semiannually.

 

i.e. Base amount = 10000

r = 8%

t = 1 year

n = 2

 

Now we know the amount is compounded semiannually and the rate of interest is 8% yearly. Hence the rate of interests semiannually will be (8%/2) i.e. 4%

 

For the 1st half year the interest earned will be,

I1 = base amount * rate

= 10000 * 4%

= 10000 * 4 /100

= 400

 

For the 2nd half year the base amount will be 10000 + 400 = 10400

And the interest earned will be,

I2 = base amount * rate

= 10400 * 4%

= 10400 * 4 /100

= 416

 

Hence the total interests earned will be,

I = I1 + I2 = 400 + 416 = 816

 

The correct answer is (C) $ 816.

 

Method 2 –

As per question –

Base amount = 10000

r = 8%

t = 1 year

n = 2

 

Total amount received at the end of year = P (1 + r/n)^nt

= 10000 (1 + (8/2)%)^(2*1)

= 10000 (1 + 4%)^2

= 10000 (1 + 4/100)^2

= 10000 (104/100)^2

= 10000 * 104 * 104/ (100 * 100)

= 104 * 104

= (100 + 4) (100 + 4)

= (100 + 4)^2

= 100*100 + 2 * 100 * 4 + 4*4

= 100000 + 400 + 16

= 100416

 

Total interests earned = Total amount received at the end of year – Base amount

= 100416 – 100000

Total interests earned = 416

 

Question 2

In a certain city, 60 percent of the registered voters are Democrats and the rest are Republicans. In a mayoral race, if 75 percent of the registered voters who are Democrats and 20 percent of the registered voters who are Republicans are expected to vote for Candidate A, what percent of the registered voters are expected to vote for Candidate A ?

(A) 50%
(B) 53%
(C) 54%
(D) 55%
(E) 57%

Solution –

Let’s assume the number of votes present in the city is X.

Number of Democrats voters,

D = 60 % X = (60 /100) * X

 

Number of Republicans voters,

R = 40 % X = (40 /100) * X

 

Expected Number of voters for candidate A = (75% of D) + (20% of R)

……(1)

(75% of D) = ( 75/100 ) * (60 /100) * X

= (3/4) (3/5) * X

= (9/20) * X

= (4.5/10) * X = 0.45X

……(2)

 

(20% of R) = (20/100) * (40 /100) * X

= 1/5 * 2/5 * X

= 2/25 * X

= 0.08 X

……(3)

 

From (1), (2), and (3)-

Expected Number of voters for candidate A = (75% of D) + (20% of R)

= 0.45X + 0.08 X

= 0.53X

= (53/100) X

= 53 % of X

 

Hence, the correct option is (B) 53%.

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