14 Simple Interest

8/2/2019 14 Simple Interest

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14

14.1 DEFINITION

PRT *Simple interest = A - P =rsn 100 (1)

If a person A borrows some money from another person B for a certain period, then after that specifiedperiod, the borrower has to return the money borrowed as well as some additional money. This additionalmoney that borrower has to pay is called interest. The actually borrowed money by A is called principal(SUM). The principal and the interest together is called amount. The injerest that the borrower has to pay..for every 100 rupees borrowed each year is known as rate per cent per annum. It is denoted as R% perRannum = 100'

The time for which the borrowed money has been used is called the time. It is denoted as T years. Theinterest is directly proportional to the principal, the rate and the time for which the borrowed sum is used.If the interest on a certain sum borrowed for a certain period is reckoned uniformly, then it is calledSimple Interest and denoted as S.l.

:. Simple Interest (S.I.) = P x 1~0 x T,where P = Principal or the sum borrowed

R = Rate per cent per annumT = Number of years for which the borrowed money has been used.

Now, simple interest + principal = amount~ Simple interest = amount - principal

If amount is denoted by 'A', then

14.2 EFFECT OF CHANGE OF P, RAND TON SIMPLE INTERESTS S' I' PRTmce, lIDp e interest = --100* Special Memory Clips for use of relation (1)

fflT lO O x ~(1) SI = -- can be rearranged as per requirement of the problem as P = , R =H){) . RT100 x S fand T = , so, in each case we find the numerator as 100 x SI and the denominator as product of other two.RT A I -ll llRllI(2) Two different cases can be compared by using the relation as A z -P2 P2R2T2

lO O x SfPT

-------


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14-2 Quantitative Aptitude for Competitive Examinationsso, if the value of P, R or T changes, then the value of simple interest (SI) will also change.It implies that /- all three parameters P, R and T may change- any two of these may change and one parameter remains fixed- anyone parameter may change and remaining two parameters are fixedIn all these cases, simple interest (SI) will change

In such cases,Product of fixed parametersChange in simple interest = x (difference of product

100 of variable parameters)Changing

Rxample: At 5% simple interest, a sum of Rs 500 fetches Rs 36 more than the amount of interest accruedon Rs 380 for the same period and rate. Find the time.elution: Here, only the principal is variable. The time and rate are fixed. Using the relation (in 14.2).

product of fixed parameters ..Change in simple interest = x (difference of product of100 variable parameters)

T x536 = -- x (500 - 380)100 '-IT = 6 years '------+ it is only difference becausethere is one variable parameterExample: The simple interest on a certain sum for 4 years at 7.5% per annum is Rs 95 less thanthe simpleinterest on the same sum for 3.5 years at r O % per annum. Find the sum._Solution: Here the principal is fixed. Let the principal (sum) be Rs PTime and rate are variable (changing)Using the relation (in 14.2),

product of fixed parametersChange in simple interest (Sl) = x (difference of product of100 variable parameters)

95 = _!!_ x (4 x 7.5 - 3.5 x 10)100P = 95 x 20 = 1900

(here, P is only fixed parameter) .

Hence, the required sum = Rs 1900- . 3 ~ A M - " : O U N T "- -PRINCfP AL (SUM)~ actually borrowed

moneySIMPLE INTEREST~ interest accrued on

the sum borrowedAMOUNT

~ money to be returnedby the borrower

+

A = Amount = Principal + Simple Interest = P T SlIn terms of principal, A = P + Sl = P + PRT = P(l + RT)

o 100 100In terms of simple interest, A = P + Sl = 100 x S1 + Sl = Sl(l + 100)

RT RT


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S im pl e I nterest 14-3

A=- P(I+ RT)= - SI (1+ 100)100 RT.>14.4 AMOUNT BECOMES N TIM ES TH E PR IN CIPA L

PRINCIPAL RATE OF INTERESTP R% p.a.

TIMET

AMOUNT BECOMESand e N xp)f ~

then, following relation is useful, /(R X T=- 100 (N-IVi

14.5 REPAYM ENT OF DEBT IN EQUAL INSTALM ENTSBORROWED (DEBT)AMOUNT=-Rs M

To be paid back in "equal" instalments. . .

Instalment no. 1 __

Instalment no. 2 --

BORROWED AMOUNT (DEBT) =-M =Instalment no. n __

ra n(n -1)na+ x---100x y 2where, r =-rate of interest per annum

y = no. of instalments per annumy = 1, when each instalment is paid yearlyy =-2, when each instalment is paid half-yearlyy =-4, when each instalment is paid quarterlyy =- 12, when each instalment is paid monthly

14.6 RATE AND TIM E ARE NUM ERICALLY EQUALHere, Rate per cent per annum =-R

Time = T numeric value of R = TPrincipal = P

Simple Interest =- SI

(hT~~J

(3)


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144 Quantitative Aptitude for Competitive ExaminationsSolved Example.

"" E-I Find the simple interest, If .\ (i) P = Rs 1,000, R = 20% per annum, T = 4 years.

(ii) P = Rs 600, R = 5% per annum, T = 4 months.(iii) P = Rs 200, R = 6% per six months, T = 3 years.(iv) P = Rs 500, R = 2% per six months, T = % years.(v) P = Rs 400, R = 3% per three months, T = 2 months.(vi) P = Rs 730, R = 10% per annum, T = 120 days.s.i

PxRxT(i) S.I. = 100 1,000x20 x 4100 =Rs 800.

( 1 ' 1 ' ) T 4 th 4= mon s = 12 year600x5x4

.. S.l. = 100 x 12 = Rs-IO.(iii) R = 6% per six months = 6 x 2 % per year = 12% per year.

/ 200 x 12 x 3:. S.I. = 100 =Rs 72.5(iv) R = 2% per six months = 4% per annum, T = 2 years, P = Rs 500

500x 4 x5:. S.I. = = Rs 50.100x22(v) R = 3% per three months = 3 x 4 = 12% per year, T = 2 months = - years.12

400 x 12 x 2:. S.l. = 100 x 12 = Rs 8.120(vi) T = 120 days = 365 year (Since 365 days = 1 year)

730 x 10 x 120. . S.l. = 100 x 365 = Rs 24.

E-2 Find the following:(i) P = Rs 100, R = 3% per annum, T = 2 year, A =?(ii) P = Rs 500, R = 6% per annum, T = 4 months, A =?(iii) P = Rs 400, R = 3.65% per annum, T = IS O days, A =?(iv) A = 540, S./. = Rs 108, R = 5% per annum, T =?

2(v) A = Rs 1,120, R = 5%, T = 25 years, S.I =?S-2 Using the formula,

(i) (Refer 14.3) A = P (1 + RT)100


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. . .

f Simple Interest 14-5 L

A =100(1+ 3X2)=100X 106 = Rs 106.100 1004

(ii) R = 6 % per annum, T = 4 months = - years.12:. A = 500 (1 + 6 x 4 ) = 500 x 102 = 510.100 x 12 100

(iii) T 150 d 150= ays = 365 year

( 3.65 x 150) 203:. A = 400 1+ = 400 x 200 = Rs 406.100 x 365

/

(iv) Using the formula,~= 100 +1S.l. RT540 (100 )-= --+1 ~T=5years.108 5 x T

[Refer 14.3J

(v) T = 2~ year = 12 years, A = 1,120, R = 5%, using the formula,5 5~ = 100 + I: 1,120 = _ _ _ _ ! Q Q _ + 1S.l. RT ' S.l. 5xl2

5. ~ 1,120 = 112S.l. 12 ~ S.I. = Rs 120.

E-3 On what sum of money lent out at 9% per annum simple interest for 6 years does the simple interest. /amount to Rs 810? (RBI '82)[Refer 14.1] Using the formula

100 x S.l. 100 x 810p=----RxTS-3

= Rs 1,500.9x6E-4S -4

(Bank PO '86)t what rate of interest per annum will a sum double itself in 8 years?[Refer 14.4], Using the formula,R x T = 100 x (N - 1); Here T = 8 yrs. N = 2 times R =?

100 1~ R x 8 = 100 x (2 - 1) ~ R = -8- = 122%.A sum when reckoned at simple interest 2!% per annum amounts to Rs 630 after 2 years. Find the2E-5 sum.S-5 [Refer 14.3],

A = P [ 1 + RT ] A = 630, P = ?100


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~-P PRIi no-p=>----1,020- P 25

14-6 Quantitative Aptitude for Competitive Examinations1 5R = 22% = 2% ' T = 2 yrs.

630 = P [1 +~] = 630 = P x 105100x2 100=> P = 600. :. The sum is Rs 600.

E-6 A sum of money lent out at simple interest amounts to Rs 720 after 2 years and to Rs 1,020 aftera further period of 5 years. Find the sum and the rate %.

S-6 Using relation (1), A - P = PRT, we find that R and P do not change here100so, ---=--A2 - P PRT2

P= 600> sum = Rs 600Putting P = 60.0 in above relation, we get

600xRx2no - 600 = 100=> R = 10Rate = 10% p.a.

E-7 Simple Interest on a certain sum is 16 over 25 of the sum. Find the rate per cent and time, if bothare equal. (UTI '90)

PxRxT 16 PxRxRS-7 S.l. = 100 => 25 x P = 100 (Since R = T given) [Refer 14.6J2 _ 1,600=> R -25 = 64 => R = 8, Hence, R = 8%, T= 8 years.

E-8 A milk man borrowed Rs 2,500 from two money lenders. For one loan, he paid 5% p.a. and for theother, he paid 7% p.a. The total interest paid for two years was Rs 265. How much did be borrowat each rate? (MBA '86)

S -8 A simple interest for the total amount = Rs 265Rate of Interest on total amount, Rm = ?

100 x S.l. 100 x 265 11R = =-%m T x P 2,500 x 2 2

7 - . ! . !Sum borrowed at 5% p.a. 2 3By Rule of Alligation, = - - = -Sum borrowed at 7% p. a. . ! . ! _ 5 12

Sum at 5% p.a.3= - - x 2,500 = Rs 1,8751+3


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Simple Interest 14-7Sum at 7% p.a.

1=-- x 2,500 = Rs .625.1+3E-9 Out of a certain sum, '!'rd is invested at 3%, . ! . th at 6% and the rest at 8%. If the simple interest for3 6

. 2 years from all these investments amounts to Rs 600, find the original sum.S-9 Rest part = 1 - G + ~) = t (BSRB '88)

Average rate % per annum on the total sum100 x Sf 100 x 600p = = = Rs 5,000.RxT 6x2

. . The original sum is Rs 5,000.E-IO What annual instalmentwill discharge a debt of Rs 4,200 due in 5 years at 10% simple interest?(AAO '82)SolO (Refer 14.5), Using the formula,

rxan(n-l)M=na+ x---100xy 2Here M = Rs 4200, n = 5, y = 1, r = 10%, a = annual instalment = ?

lOxa 5x44,200 = Sa + 1."00 x -2- => 4,200 = 6a=> a = Rs 700 per year.E-ll A sum of Rs 2 is lent to be paid back in 3 equal monthly instalments of Re. 1 each. Find the rate

'\ per cent.,S-U (Refer No. 14.5), Using the formula,r x a n(n-l)M= na + x--~100 x y 2

Here M = Rs 2, a = Re 1, n = 3, y = 12, r = ?r x l 3x22 = 3 X 1+ x -- => r = 400%.l00x 12 2

:. The rate % p.a. is 400%.E-12 If Rs 85 amounts to Rs 95 in 3 years, what Rs 102 will amount to in 5 years at the same rate per

cent? (MBA '81)S-12 [Refer 14.1], Using the formula (1) we get, P1 X R1 X T1P1 X R2 X T2

Here, A2 -10295-85 85 x R X 3 => A 102 = 20,102 x R x 5 2 - => A2 = 122.

The amount is Rs 122.


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14-8 Quantitative Aptitude for Competitive ExaminationsE-13 A sum was put at simple interest at a certain rate for 4 years. Had it been put at 2% higher rate,

it would have fetched Rs 56 more. Find the sum. (Bank '89)S-13 Here rate % p.a. is changed, so, value of simple interest also changes. [Refer 14.2Jcr" . _ Product of FIXED parameter [difference of product Of]Change m simple mterest - 100 x VARIABLE parameter

where, fixed parameters are P and T, given, T = 4 years.only one variable parameter is R , given, R ! - R 2 = 2also, given, Sf! - Sf2 = Rs 56.Px4=> 56 = 100 [2] => P = 700.:. The sum is Rs 700.

E-14 A sum of Rs 3,800 is lent out in two parts in such a way that the interest on one part at 8% for 5years is equal to that on another part at % for 15 years. Find ~he sum lent out at 8%.

1S-14 Let the sum lent out at 8% = P I; sum lent out at 2% = P2since (SI)I = (Sfh

\

1PI X 8 x 5 = P 2 X - x 15 =>2P I 15 3P 2 2x8x5 163(3 + 16) x 3,800 = Rs 600.. PI = Sum lent out at 8%

I REGU':!R PRO~lEMS I(1) At what rate per cent per annum a sum of Rs 1,800 will become Rs 2,700 in 10 years?

(a) 5% (b) 6% (c) 10% (d) 6.75% (e) None of these(2) A sum of Rs 1,600 lent at simple interest of 12.5% per annum will become twice in (Bank '81)

(a) 6 years (b) 71ears (c) 8 yrs. (d) 91rs. (e) None of these2 4(3) Rakesh took a loan for 6 years at 5% p.a. simple interest. If the total interest paid was Rs 1,230, the

principal was(a) Rs 4,100 (b) Rs 5,000 (c)Rs 5,300 (d)Rs 4,920 (e)None of these

(4) If Rs 1,200 amounts to Rs 1,440 in 5 years at simple interest, the rate % p.a. is(a) 10% (b) 12% (c) 4% (d) 5% (e) None of these

(5) If a sum of Rs 1,600 gives a simple interest of Rs 252 in two years and 3 months, then the rate %p.a. is

1(a) 52% (b) 8% (c) 7% (d) 6% (e) 5%(6) Inwhat time will Rs 72 become Rs 81 at 6 i % p.a. simple interest?

(a) 1 yr 6 months (b) 2 yrs.(MBA '79)

(c) 2 _ ! _ yrs.4(d) 21 yrs.2 (e) 1 year


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Simple Interest 14-9(7) A sum of money doubles itself in 10 years at simple interest. Inhow many years would it treble itself?

(Bank PO '78)(a) 10 (b) 15 (c) 20 (d) 25 (e) None of these

(8) At what rate per cent (simple interest) will a sum of money double itself in 16 years?1(a) 50% (b) 5% (c) 64% (d) 10% (e) 20%

(9) On retirement, a person gets 1.53 lakhs of his provident fund which he invests in a scheme at 20%p.a. His monthly income from this scheme will be(a) Rs 2,450 (b) Rs 2,500 (c) Rs 2, 550 (d) Rs 2,600 (e) Rs 2,700Find out the capital required to earn a monthly interest of Rs 600 at 6% simple interest.(a) Rs 1.0 lakhs (b) Rs 1.2 lakhs (c) Rs 1.1 lakhs(d) Rs 1.3 lakhs (e) None of theseA sum of money lent out at simple interest amounts to Rs 2,520 in 2 years and Rs 2,700 in 5 years.Find the rate % p.a. 1(a) 3% (b) 4% (c) 2-% (d) 5% - (e) None of theseA sum of money doubles itself in 7 yrs. In ffow many years it becomes four fold?(a) 10 yrs. (b) 35 yrs. (c) 14 yrs. (d) 21 yrs. (e) 28 yrs .

(10)

(12). . .RTI N,-lHint : Use -- =--, RT2 N2-1

7 2-1-=--(13) I gave some money at simple interest and at the end of 10 yrs, got back twice the sum. The rate %

p.a. was(a) 2% (b) 4% (c) 5% (d) 10% (e) 20%Hint : Use RT = (N - 1) x 100.

(14) A man pays 40 times the annual rent to purchase a building. The rate % p.a. he derives from hisinvestment is(a) 25% (b) 2.5% (c) 5% (d) 40% (e) 4%Tips: Rate% p.a = 100 %.No. of times the annual rent

(15) If Re 1 produces Rs 9 in 60 years at simple interest, the rate % p.a. is1 1(a) 133% (b) 14% (c) 15% (d) 122%

Hi~ investment (P) = 1 Re S./. = Rs 9.(16) If Re 1 becomes Rs 9 in 60 years at simple interest, the rate % p.a. is

(e) None of these

(d) 12 % (e) None of thesea) 15%Hint : If investment (P) = Re 1 then S .f = 9 - 1 = Rs 8.

(17) If x is the simple interest on y and y is the simple interest on z, the rate % and the time being thesame in both cases, what is the relation between x , y and z? (MBA '80)(a) x2 = yz (b) l= xz (c) l xy (d) xyz = 1 (e) x = 2y + z


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14-10 Quantitative Aptitude for Competitive Examinations(18) The simple interest on a sum of money is _! of the principal and the number of years is equal to the- 9rate % p.a. The rate % p.a. is

1 1(a) 3% (b) 3 : ( Y o (c) 10% (d) 3% (e) 9%.The simple interest on a certain sum of money at 4% p.a. for 4 years is Rs 19 more than interest onthe same sum for 3 years at 5% p.a. Find the sum of money(a) 6,700 (b) 7,500 (c) 8,000 (d) 8,750 (e) 9,500The simple interest on Rs 800 at 6% per month for 9 months is(a) Rs 51.60 (b) Rs 36 (c) Rs 432 (d) Rs 360 (e) None of theseIf Rs 450 amount to Rs 540 in 4 years, what will it amount to in 6 years at the same rate %?(a) Rs 600 (b) Rs 585 (c) Rs 700 (d) Rs 640 (e) None of theseTips: Since Principal and Rate are same in both cases; So, simple interest per year will be the same.This concept is used here.The interest- on a sum of money at the end of 2 -21years is iof the sum. The rate per cent per year is5 (a) 10% (b) 20% (c) 16% (d) 32% (e) 40%A man lent Rs 600 for 2 years and Rs 200 for 3 years, at the same rate at simple interest and receivedonly Rs 90 as interest. What was the rate % p.a.?

\(19)

(20)(21)

(22)

(23)

(a) 12% (b) 5% (c) 6% (d) 8_!%3 (e) 4%

Hint: Rate is same :.(24) A certain sum of money amounts to ~ of itself in 5 years. The rate per cent p.a. is4

(a) 10% (b) 5% (c) 7% (d) 11%(25) Inwhat time will a sum of money double itself at 3% per annum at simple interest?

(a) 331yrs. (b) 30 yrs. (c) 131yrs. . (d) 6 yrs. (e) 231yrs.3 3 3(26) Namrata deposited Rs 8,000 which amounted to Rs 9,200 after 3 years at simple interest. Had the

interest been 2% more, she would get how much?(a) Rs 1,680 (b) Rs 9,860 (c) Rs 9,980 (d) Rs 9,680 (e) Rs 10,620

(27) v= rate of interest on a sum of money is 3% p.a. for the first four years, 5% p.i for the next four.years and 6% p.a. for the period beyond 8 years. If the simple interest accrued on the sum for a totalperiod of 9 years is Rs 817, the sum is(a) Rs 21.50 (b) Rs 18.50 (c) Rs 29.00 (d) Rs 215 (e) None

(28) What quarterly payment will discharge a debt of Rs 2,280 due in two years at 16% p.a. simpleinterest?(a) Rs 1,000 (b) Rs 1,600 (c) Rs 250 (d) Rs 360 (e) Rs 450

(Bank PO, '89)Answers1. (a) 2. (c) 3. (a) 4. (c) 5. (c) 6. (b) 7. (c) 8. (c) 9. (b)10. (b) 11. (c) 12. (d) 1 3 . (d) 14. (b) 15. (c) 16. (c) 17. (b) 18. (b)19. (c) 20. (c) 21. (b) 22. (d) 23. (b) 24. (b) 25. (a) 26. (d) 27. (e)28. (c)

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14 Simple Interest