Simple and Compound Interest 05-09-12

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SIMPLE AND COMPOUND INTEREST ★

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Interest is the money that paid for the use of a certain amount. The amount borrowed is called the Principal. The sum of interest and principal is called the Amount.

SIMPLE INTEREST If the interest is calculated on original Principal for a certain period is called the Simple Interest (S.I.). Simple Interest will be the same for all the years. If P is the principal, R is the rate of interest, interest, T is the time and S.I. S.I. the simple interest, interest, then PTR Simple Interest =  ⎯⎯  100 TR Amount = P 1+  ⎯⎯  100 e.g: Find the Simple Interest obtained on an

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the principal for the next period, then the money is said to be lent at Compound Interest. Thus the amount at the end of period becomes the principal for the next period. If A is the amount, C.I. is the Compound Compound Interest, P is the principal, principal, R is the rate, and T is the time, then R T A = P 1+ ⎯  100

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R T C.I. = P 1 +  ⎯  − P 100 e.g: What is the Compound Interest accrued on an amount of Rs. 8000 at the rate of 5 p.c.p.a. at the end of 3 years?

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R T C.I. = P 1 +  ⎯  100

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1 amount of Rs.16800 at the rate of 4  ⎯  2 p.c.p.a. for a period of 3 years

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5 3 C.I. = 8000 1 +  ⎯  − 8000 100 ⇒

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105 105 105  ⎯   ⎯   ⎯  ] 100 100 100

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8000

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Difference 61 = P× 8000 @ 10% Difference = 31 P× 1000 e.g: What is the difference between Simple and Compound Interest Rs.42800 for two years at 5% rate?

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P × R2 42800 × 25 Difference =  ⎯⎯ ⇒ = Rs.107 1002 10000 e.g: On what sum does the difference between Simple and Compound Interest for 3 years at 10% rate will be Rs.403? P × 31 P × 31 ⇒ Sol: Difference = 403 = 1000 1000 403 × 1000 ⇒ P= Rs. 13000 31 1. A certain sum of money becomes becomes Rs.1250

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= Rs.1261

Short cut: If we can observe 8% for 3 years on 1st part is 24% and 6% for 4 years on 2 nd part is also 24%. Interest on both parts are equal means both 1 st and 2nd parts are equal. 3. A sum of money amounts amounts to Rs.1488 Rs.1488 in 3 years at a Simple Interest. If the rate of interest is raised by 25%, the sum amounts to Rs.1560 during the same period. Find the sum and the rate of interest. Sol: Rs.1560 - Rs.1488 = Rs.72. 25% of interest = Rs.36 100 ∴ 100% interest =  ⎯  × 72 = Rs.288 Rs.288 25 The interest for 3 years = Rs.288. Principal = 1488 - 288 = Rs.1200 288 × 100 ∴ Rate = = 8% 1200 × 3 4. A sum of money invested at Compound Compound Interest amounts to Rs.650 at the end of first year and Rs.676 at the end of second year. Find the rate of interest. Sol: Interest in 2nd year = 676 - 650 = Rs.26 As this is Compound Interest, 2 nd year interest is calculated on1 st year amount 26 ∴ Rate of interest = × 100 = 4% 650 ∴

How much does he get as interest? Sol: Here P = Rs.16800 Rs.16800,, T = 3 years 1 9 R = 4  ⎯ % =  ⎯ % 2 2 16800 × 3 × 9 Simple Interest = = Rs. 2268 2 × 100

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e.g: What principal will amount to Rs.5700 at 1 4% per annum in 3  ⎯  years? 2 TR Sol: Amount = P 1 +  ⎯⎯  100

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7×4 P 1 +  ⎯⎯  = 5700 2 × 100 5700 2 100  ⎯⎯⎯  = Rs. 5000 228

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in a span of 5 years and further to Rs.1700 in the span of 8 years at the same rate of Simple Interest. What would be the amount at the end of 12 years? Sol: Interest for 3 years (8 - 5 years) QUANTITATIVE APTITUDE = 1700 - 1250 = Rs.450 5 G.S. Giridhar Interest for 5 years = — × 450 Shortcut: Amount = 105% of 105% 3 of 105% of 8000 = Rs. 9261 = Rs.750 ∴ C.I. = 9261 − 8000 = Rs.1261 Principal = 1250 - 750 = Rs.500 Note: ★ If the Interest is paid half yearly, time 12 Interest for 12 years = — × 450 = Rs.1800 is doubled and the rate is halved. 3 ★ If the Interest is paid quarterly, time ∴ Amount after 12 years = 500 + 1800 becomes 4 times and the rate becomes = Rs.2300 one -fourth 2. An amount of Rs.15600 is to be divided into Difference between Simple two parts such that the Simple Interest on and Compound Interest the first part at 8% p.a. for 3 years is equal to It can be calculated by the following the Simple Interest on the second part at 6% formulae. p.a. for 4 years. What is the difference between the two parts? ★ For one year: There is no difference. Sol: Let the first part be Rs. x  and 2nd will be P × R2 Rs.(15600 - x ) ★ For 2 years: Difference =  ⎯⎯  1002  x  × 8 × 3 (15600 - x ) × 6 × 4 (300 + R) P × R2  ⎯⎯⎯⎯  = 100 100 ★ For 3 years: Difference =  ⎯⎯⎯⎯  2 x  = 15600 1003 15600 If the rate of interests are 5% and 10%, the ⇒ x  =  ⎯⎯⎯⎯  = Rs.7800 2 following formulae can be used Both parts are equal so there is no difference @ 5%

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(Writer - Director, RACE Institute, Hyderabad) Hyderabad)

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Shortcut: For one year, rate of interest is 4% 1 1 and for 3 ⎯  years it is 4 × 3 ⎯  = 14% 2 2

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