SHORT METHOD for Difference between C. I & S. I for 3 years C. I

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1 SIMPLE INTEREST S. I = PTR S. I = Simple interest P = principal T = time in years R = rate of interest A = P + S. I A = total amount COMPOUND INTEREST C. I = P (1 + R )T P C.I = Compound interest P = principal T = time in years R = rate of interest A = P + C. I A = Total amount Compound interest for half yearly C. I = P (1 + R 2 )2T P Compound interest for quarterly C. I = P (1 + R 4 )4T P When T = 2 years, R = any rate of interest C. I S. I = PR2 2 When T = 3 years, R = any rate of interest C. I S. I = PR2 (300+R) 3 EXAMPLE: The difference between Compound and Simple rates of interest on 10, 000/- for 3 years at 5% per annum is.. SOLUTION : SHORT METHOD for Difference between C. I & S. I for 3 years C. I S. I = PR2 (300+R) 3 10, (300 +5) = 3 = (answer)

2 SHORT METHODS FOR COMPOUND INTEREST When T = 2 years R = any rate of interest For example R = 6% C. I = Compound interest P = principal For example R = 8% When T = 3 years, R = 3% C. I = P When = 3 years, R = 4% C. I = P When T = 3 years, R = 5% C. I = P When T = 3 years, R = 6% C. I = P When T = 3 years, R = 7% C. I = P When T = 3 years, R = 8% C. I = P When T = 3 years, R = 9% C. I = P When T = 3 years, R = 10% C. I = P 33.1 When T = 3 years, R = 11% C. I = P

3 When T = 3 years, R = 12% C. I = P When T = 3 years, R = 13% C. I = P When T = 3 years, R = 14% C. I = P When T = 3 years, R = 15% C. I = P On simple interest any amount becomes 812/- in two years and 924/- in four years. What is the rate of interest on that amount? S.I = PTR/ & A = S.I + P Simple interest (S.I) => = 112/- Principal (p) => S.I = PTR/ => R= S.I PT 112 = R = 8% (answer) 2 A man deposits am amount of 54600/- at a S.I rate of 12% for 3 years. What total amount will he get at the end of 3 years? Short method: 12 3 = 36% If % money % ( + 36)..? Total amount (A) = = 74256/- (answer) 3 A sum of money will become /- in four years at 7% per annum on S.I. Find the sum.. Short method 7 4 = 28% If 128% ( + 28) %?

4 Principal (P) = 128 = 85000/- (answer) 4 A sum of money will become double in 3 years at a certain rate of C.I. In what time will it becomes four times itself? Short method In 3 years becomes double In 6 years (3+3) becomes 4 times (double double) Therefore, Answer = 6 years 5 What will be the amount on 25000/- in 2 years at C.I if the rates for the successive years be 4% & 5% per year Short method: Total amount (A) = A = 27300/- (answer) 6 The difference of S.I on 5000/- from two banks in 2 years is /-. Find the difference of their rate Given that, P = 5000/- T = 2 years S.I = /- Formula S. I = P T(R1 R2) (R1 R2) = R1 R2 = 1% (answer) 7 A sum becomes 3 times in 10 years. In how many years will amount to 5 times at the same rate of S.I. Formula, T2 = (Y 1) T 1 X 1 Given that, X = 3 times, Y = 5 times, T 1 = 10 years & T 2 =? (5 1) 10 T 2 = 3 1 T2 = 20 years (answer) 8 Find the sum which amount to 1125/- in 5 years and becomes 1200/- in 8 years at the rate of S.I

5 Formula P = [A2 ( T 1 ) (A T 2 T 2 A 1 )] 1 Given that, A 1 = 1125/-, A 2 = 1200/-, T 1 = 5 years, T 2 = 8 years & P =? P = [1125 ( 5 ) ( )] 8 5 P = 0/- (answer) 9 If 5, 000/- becomes 5, 700/- in one year, what will 7, 000/- become at the end of 5- years at the same rate of simple interest? S. I = 5, 700-5, 000 = 700/- S. I = PTR 700 = R = 14% NOW S. I = PTR S. I = R = 4, 900/- Total money=> 7, , 900 = 11, 900/- (answer) 10 A sum of money 12, 000/- deposited at compound interest became double after 5- years. How much will it be after 20 years? SHORT METHOD 5 (If in 5- years).. 2 times times times times Required answer, 12, = 1, 92, 000/- (answer) 11 If the difference between the C. I, compounded every 6 months and the S. I on certain sum of money at the rate of 12% p. a for one year is 36/-, the sum is Formula, D = PR2 2 Here, R = R = 6% 2 2 P = P = 10, 000/- (answer) => 12

6 NOTE: As the interest was compounded half- yearly, we changed R to R 2 T 2 and T to 12 Arun lends 20, 000/- to two of his friends. He gives 12, 000/- to the first one at 8% per annum at simple interest. Arun wants to make a profit of 10% on the whole. The simple interest rate at which he should lend the remaining sum of money to the second friend is S. I on 12, 000/- => = 960/- Desired gain on 20, 000/- = 20, = 2, 000/- S. I on 8, 000 => 2, = 1040/- Therefore, S. I = PTR 1040 = R R = 13% (answer) 13 An amount of money at C. I grow up to 3840/- in 4- years and up to 3956/- in 5- years. Find the rate of interest FORMULA R = [ ( A 2 A 1 ) 1 T2 T1 1 ] R = [ ( ) ] R = 2. 5% (answer) 14 A man borrows 21, 000/- at 10% compound interest. How much he has to pay equally at the end of each year, to settle his loan in two years is Let annual payment = X x ( )2 By solving, we get x = 12, /- (answer) x ( )2 = 21, , 500/- is invested at a rate of 10% S. I and interest is added to the principal after every 5- years. In how many years will it amount to 2, 500/-?

7 First we will find the S. I for 5- years S. I = PTR S. I = = 750/- Now principal after 5- years => 1, = 2250/- Final amount = 2500/- (given) S. I= = 250/- S. I = PTR 250 = 2250 T 10 T = 10 years 9 Therefore, total time => = (answer) 9 16 What annual payment will discharge a debt of 6450/- due in 4- years at 5% per annum simple interest? Let the annual installment = X X + (X + X 3 5 ) + (X + X 2 5 ) + (X + X 1 5 ) = 6450 X = 1500/- (answer) 17 A person invested in three banks in the ratio of 1: 2: 3 and the rates were in the ratio of 2: 3: 4 at S.I, also he got the income in the ratio of 3: 4: 5, then find the ratio of time periods S.I = PTR S.I T = PR Therefore, the ratio of time periods T1 : T2 : T3 = T1 : T2 : T3 = S1 P1 R = 18: 8: 5 (answer) S2 P2 R S3 P3 R A person invested in all 2, 600/- at 4%, 6% and 8% per annum S.I. At the end of the year, he got the same interest in all three cases. The money invested at 4% is Let the amount interested at 4%, 6% and 8% per annum S.I are X, Y and Z respectively

8 S.I = PTR S. I = x 1 4 X: Y: Z = = 6: 4: 3 1 S. I = y : 1 6 : 1 8 Therefore, X = S. I = z 1 8 = 1200/- (answer) 19 A person has 5, 000/-. He invests a part of it at 3% per annum and the remainder at 8% per annum S.I. His total income I 3- years is 750/-. Find the sum invested at different rate of interest. Average rate of interest => S.I = PTR 750 = R R = 5% By using Allegations and mixture method Required ratio = 3: 2 Investment at 3% per annum = 3, 000/- (answer) Investment at 8% per annum = ( ) 5000 = 2, 000/- (answer) = ( ) The S.I and C.I on a sum of money for are 8, 400/- and 8652/- respectively. The rate of interest per annum is SHORT METHOD for 2- years R = 6% (answer) S. I C. I = 200 R R = 200 R R 21 A sum of money invested at C.I amounts to 800/- in 2- years and 880/- in 3- years. Find the rate of interest per annum and the sum

9 SHORT METHOD Here, A 1 = 800/- A 2 = 880/- For rate of interest = 10% (answer) And Sum = A 1 ( A 1 A 2 ) T = 800 ( )2 = /- (answer) A2 A1 = A = A man borrows 3000/- at 10% compound rate of interest. At the end of each year he pays back 0/-, how much amount should he pay at the end of the third year to clear all his dues. C. I for 1 st year = S. I for 1 st year = 10% of 3000 = 300/- Principle for 2 nd year = ( ) 0 = 2300/- C. I for 2 nd year = S. I of 2300 at 10% = 230/- Principle for 3 rd year = ( ) 0 = 1530/- C. I for 3 rd year = 10% of 1530 = 153/- Therefore, total amount pay at the end of 3 rd year = = 1683/- (answer) 23 A certain sum is invested for certain time. It amounts to 450/- at 7% per annum. But, when invested at 5% per annum, it amounts to 350/-. Find out the sum and time. Using the formula, p = A 2R 1 A 1 R 2 R 1 R 2 Here A 1 = 450/-, R 1 = 7%, A 2 = 350/-, R 2 = 5% P = /- P =

10 A 1 A 2 Also using the formula, T = [ ] A 2 R 1 A 1 R T = [ ] T = 50 years (answer) 24 A sum 2/- is lent to be paid back in 3 equal monthly instalments of 1/- each. Find the rate percent. Using the formula, Z = na Ra n(n 1) b 2 Here, Z = debt to be paid = 2/-, a = 1/-, n = 3 R =? b = number of installments per year = 12 R = 400% (answer) 2 = 3 1 R A man borrows 3, 000/- at 10% compound interest per annum. At the end of each year he pays back 1, 000/-. How much amount he pay at the end of 3rd year to clear all his dues? Amount due at the end of 1 st year = ( ) 0 = 2, 300/- Amount due at the end of the 2 nd year = ( ) 0 = 1, 350/- Amount due at the end of the 3 rd year = = 1683/- (answer) 26 Divide 15, 494/- A and B so that A s share at the end of 9 years may be equals to B s share at the end of 11 years, Compound Interest being 20% per annum. Then A s share is.. Let A s share = x & B s share = 15, 494 x According to question x ( )9 = (15, 494 x) ( )11 X = 9, 144/- (answer)

11 27 The Simple Interest for 4 years is one fourth of the Principal. The sum that will be amount to 450/- in two years at the same rate is.. Let the Principal be P/- According to question S. I = P T R R = 25 % Per annum 4 [Formula] P 4 = P 4 R P = P = S.I R T [Formula] (450 P) [From question] By solving, we get P = 400/- (answer) 28 Kartik lost 9% by selling pencils at the rate of 15 a rupee. How many for a rupee must Kartik sell them to gain 5%. PERCENTAGE METHOD: = x 105 x = 13 (answer)

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