SIMPLE INTEREST and COMPOUND INTEREST

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Alyson Webb
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1 SIMPLE INTEEST a COMPOUND INTEEST (For all Competitive Exams) Theory: Moey borrowe by a borrower or the moey le by a leer is calle the pricipal (P). The time for which it is borrowe or let is calle time perio (T). The extra moey pai by the borrower to the leer is calle the iterest. Iterest is efie as rate () per cet per aum (p.c.p.a.). If the iterest is pai oly o the pricipal for every year the it is calle simple iterest (I). Simple iterest (I) o a sum of s P borrowe at % p.a. for T-years is give by The total moey pai by the borrower to the leer to clear the ebt is calle amout (A) a it is equal to P + I. PT + T A P + I P + P A P + T If the iterest is calculate o the previous year s amout istea of pricipal except for the first year the it is calle a compou iterest. If a sum of s P is let out for -years at % p.a. compou iterest the the amout receive is give by A P The compou iterest eare (C.I) A P C.I P P P Some importat formulae: (i) If a sum of moey becomes x-times of itself i % p.a. I. the (x -) T (ii) If a sum of moey becomes -times of itself i a time of % p.a. x T I. it becomes -times of itself i % p.a. I. the x T (iii) A sum (P) of moey becomes a amout of i years at a certai rate a the same sum becomes a amout of i years ( ). The P AT AT a the rate T T ( A P) () PT (iv) If the rates of compou iterest are,,.. for -successive years the

2 A P... (v) If a sum of s P is let out at % p.a. compou iterest for -years the A P, if the iterest is compoue half-yearly 00 4 P, if the iterest is compoue quarterly 400 (vi) The ifferece betwee compou iterest a simple iterest o a sum of s P for -years at % p.a. is give by P I Also, where I is simple iterest for years 00 (vii) The ifferece betwee compou iterest a simple iterest o a sum of s P P ( + 00) I ( + 00) for years at % p.a. is give by where I. is simple iterest for -years (viii) If a sum of moey amouts to A a to A i ( ) a years respectively the A A A. POBLEMS. At what rate will a ma get o simple iterest of `,07 o a pricipal of `,550 i years? a) p.c.p.a. b) 4 p.c.p.a. c) 6 p.c.p.a. ) 8 p.c.p.a. e) Noe of ANSWE: b P 550, I 07, T,? PT I The simple iterest accrue i 5 years o a pricipal of ` 4,000 is oe-teth the pricipal. What is the rate of simple iterest p.c.p.a.? a) 5 b) 4 c) 6 ) e) Noe of ANSWE: P 4,000 P I,400 0 T 5?

3 . A let ` 5000 to B for years a ` 000 to C for 4 years o simple iterest at the same rate of iterest a receive ` 00 i all from both as iterest. The rate of iterest per aum is a) 7% b) 5% c) 7 % 8 ) 0% e) Noe of ANSWE: Let the rate of iterest be x i each case the the total iterest 5000 x x + 00 x + 0 x x Shamita took a loa at simple iterest rate of 6 p.c.p.a. i the first year a it icrease by.5 p.c.p.a. every year. If she pays ` 8,90 as iterest at the e of years, what was her loa amout a) ` 6000 b) ` 5400 c) ` 6800 ) ca t be etermie e) Noe of ANSWE: e P? I 890 P ( But I + + P ( ).5 P P What woul be the compou iterest obtaie o a amout of ` 6,000 at the rate of 7 p.c.p.a. for years? a) ` b) ` 846. c) ` ) ` e) Noe of ANSWE: e P C.I? C.I P 7 07 C.I What is the compou iterest o ` 5,000 for 4 years if the rate of iterest is 0% p.a. for the first years a 0% p.a. for the ext years? a) `,0.50 b) `,7 c) `,745 ) ` 5,68 e) Noe of ANSWE: P

4 A P 0 0 A C.I A sum of moey iveste at compou iterest amouts to ` 650 at the e of first year a ` 676 at the e of seco year. The sum of moey is: a) ` 600 b) ` 540 c) ` 65 ) ` 560 e) Noe of ANSWE: c A 650 A 676? A A A % A P P P The ifferece i simple a compou iterest o a certai sum for years at 5% per aum compoue aually is ` 75. Fi the sum? a) ` 40,000 b) ` 0,000 c) ` 50,000 ) ` 0,000 e) Noe of ANSWE: P 75 P P , Two customers borrowe the same amout of moey, oe at compou iterest a at the other at simple iterest. If after two years, the iterest payable by oe was ` 0 a the other ` 00, the what was the priciple moey let to each of them? a) ` 450 b) ` 500 c) ` 550 ) ` 575 e) Noe of ANSWE: b I 00 P? I 00 Also P

5 0 0 P P If the compou iterest o a certai sum for years at % per aum is ` 0.50, the the simple iterest o the same sum at the same rate a for the same time will be? a) ` 90 b) ` c) ` ) ` 98.5 e) Noe of ANSWE: c I x I x x C.I I + x 0x 0.5 x x 0

SIMPLE INTEREST, COMPOUND INTEREST INCLUDING ANNUITY

Chapter SIMPLE INTEREST, COMPOUND INTEREST INCLUDING ANNUITY 006 November. 8,000 becomes 0,000 i two years at simple iterest. The amout that will become 6,875 i years at the same rate of iterest is:,850