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 True Discount Questions

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FACTS  AND  FORMULAE  FOR  TRUE  DISCOUNT  QUESTIONS

 

 

Suppose a man has to pay Rs.156 after 4 years and the rate of interest is 14% per annum. Clearly, Rs. 100 at 14% will amount to Rs. 156 in 4 years. So, the payment of Rs. 100 now will clear off the debt of Rs.156 due 4 years. Hence, we say that :

 

Sum due = Rs.156 due 4 years hence;

 

Present Worth (P.W) = Rs. 100;

 

True Discount (T.D) = (Sum due) - (P.W)=Rs. (156 - 100) = Rs. 56

 

We define : 

               T.D = Interest on P.W  

               Amount = (P.W) + (T.D)

Interest is reckoned on P.W and true discount is reckoned on the amount.

 

IMPORTANT FORMULAE

Let rate = R% per annum and Time = T years. Then,

1. P.W=100×Amount100+R×T=100×T.DR×T

 

2. T.D=P.W×R×T100=Amount×R×T100+R×T

 

3.  Sum=S.I×T.DS.I-T.D

 

4. (S.I) - (T.D )= S.I on T.D

5. When the sum is put at compound interest, then 

P.W=Amount1+R100T

Q:

The true discount on a bill due 9 months hence at 16% per annum is Rs. 189. The amount of the bill is

A) 1200 B) 1764
C) 1600 D) 1354
 
Answer & Explanation Answer: B) 1764

Explanation:

ke

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13 11659
Q:

The present worth of Rs.1404 due in two equal half-yearly instalments at 8% per annum. Simple interest is:

A) 1320 B) 1300
C) 1325 D) 1200
 
Answer & Explanation Answer: C) 1325

Explanation:

Required Sum = PW of Rs.702 due 6 months hence + PW of Rs.702 due 1 year hence 

= Rs.[ (100 x 702) / (100+(8 x 1/2)) ] + [ (100 x 702) / (100+(8 x 1)) ]  

= Rs.1325

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10 10967
Q:

If the true discount on s sum due 2 years hence at 14% per annum be Rs. 168, the sum due is ?

A) Rs.948 B) Rs.876
C) Rs.768 D) Rs.658
 
Answer & Explanation Answer: C) Rs.768

Explanation:

P.W. = 100×T.DR×T = 100×16814×2 = 600.

Sum = (P.W. + T.D.) = Rs. (600 + 168) = Rs. 768.

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Exam Prep: CAT , Bank Exams , AIEEE
Job Role: Bank PO , Bank Clerk

16 10929
Q:

The interest on Rs.750 for 2yrs is the same as the True Discount on Rs.960 due 2yrs hence . If the rate of interest is same in both cases,it is:

A) 12% B) 14%
C) 15% D) 16
 
Answer & Explanation Answer: B) 14%

Explanation:

S.I on Rs.750= T.D on Rs. 960 

This means P.W of Rs. 960 due 2 years hence is Rs.750 

Therefore , T.D= Rs. (960 - 750) = Rs. 210 

Thus, S.I on Rs. 750 for 2 years is Rs. 210 

Rate =[ (100 x 210) / (750 x 2) ] % = 14%

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1 9036
Q:

The Present worth of Rs.2310 due 212 years hence ,the rate of interest being 15% per annum, is :

A) Rs.1440 B) Rs.1750
C) Rs.1680 D) Rs.1840
 
Answer & Explanation Answer: C) Rs.1680

Explanation:

P.W=Rs.100×2310100+15×52 = Rs.1680

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0 8255
Q:

A bill falls due in 1 year.The creditor agrees to accept immediate payment of the half and to defer the payment of the other half for 2 years.By this arrangement ins Rs.40.what is the amount of the bill,if he money be worth 12.5%?

A) 1200 B) 3000
C) 3600 D) 1300
 
Answer & Explanation Answer: C) 3600

Explanation:

Let the sum be Rs. x. Then,   

x2+x2×100100+252×2-x×100100+252×1 = 40  

(x/2)+(2x/5)-(8x/9) = 40  

x=3600.  

Therfore, amount of bill=Rs. 3600.

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5 7446
Q:

The True discount on Rs1760 due after a certain time at 12% per annum is Rs160. The time after which it is due is?

A) 15months B) 5months
C) 12months D) 10months
 
Answer & Explanation Answer: D) 10months

Explanation:

P.W = Rs. (1760 - 160) = Rs.1600  

S.I on Rs.1600 at 12% is Rs. 160 

Time = (100 x 160)/(1600 x 12)  = 5/6 years = (5/6) x 12 months = 10 months

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1 7293
Q:

A has to pay Rs.220 to B after 1yr. B asks A to pay Rs.110 in cash and defer the payment of Rs.110 for 2 yrs. A agrees to it. If the rate of interest be 10% per annum in this mode of payment:

A) A gains Rs.11 B) There is No gain or loss
C) A losses 7.43 D) A gains Rs. 7.34
 
Answer & Explanation Answer: D) A gains Rs. 7.34

Explanation:

A has to pay = Present worth of Rs220 due 1yr hence  

= Rs.[(220 x 100)/100+(10 x 1)] = Rs.200 

 

A actually pays = Rs.110+PW  of Rs.110 due 2 yrs hence 

= [110+(110 x 100)] / [100+(10 x 2)] = Rs.192.66  

 

So, A gains Rs. (200-192.66) = Rs.7.34

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4 7237