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SIMPLE AND COMPOUND INTEREST 

1. Akshay borrows a sum of Rs.70,000 at 10% pa compound interest. He repays a certain amount at the end of one year and the balance amount of Rs.44,000 at the end of the second year. What amount does he repay in the first year?
A) 29,000     B) 65,000     C) 37,000    D) 45,000    E) 30,000
Sol: Sum = Rs. 70,000

 

2. What is the compound interest (in Rs.) accrued on an amount of Rs. 30,000 at the rate of 20 percent annum in two years, if the
interest is compounded half-yearly?
A) 14,527     B) 16,524     C) 12,654      D) 13,923     E) 11,253
Sol: Ratio Method:
T = 2 Years
Half yearly T = 2T = 2(2) = 4

 

3. The difference between the compound interest and simple interest on a certain sum at 20% per annum for 2 years is Rs. 3,600. Find
the sum....
A) Rs.72,000    B) Rs.90,000     C) Rs.80,000     D) Rs.85,000     E) Rs.95,000
Sol: To solve this question, we can apply a short trick approach
When the Difference is for 2 years

 

4. The difference between the compound interest and simple interest accrued on an amount of Rs.18,000 in 2 years was Rs.2,880. What was the Rate of interest p.c.p.a.?
A) 42%        B) 35%         C) 40%        D) 45%       E) 60%
Sol: To solve this question, we can apply a short trick approach
When the Difference is for 2 years

 

5. The difference between simple and compound interests compounded annually on a certain sum of money for 2 years at 15% per annum is Rs.324. The sum (in Rs.) is:
A) 14,400     B) 18,000     C) 16,000        D) 17,500      E) 19,500
Sol: To solve this question, we can apply a short trick approach
When the Difference is for 2 years

 

6. What will be the compound interest on a sum of Rs. 40,000 after 3 years at the rate of 20 p.c.p.a.?
A) Rs. 30,000     B) Rs. 29,120     C) Rs.31,120      D) Rs. 15,120     E) Rs. 35,120
Sol: Ratio Method:

 

7. The difference between compound interest and simple interest on an amount of Rs. 30,000 for 2 years is Rs. 147. What is the
rate of interest per annum?
A) 12%     B) 10%     C) 9%     D) 7%        E) 8%
Sol: To solve this question, we can apply a short trick approach
When the Difference is for 2 years

 

8. A sum of money at simple interest amounts to Rs.840 in 3 years and to Rs.900 in 4 years. The sum is:
A) Rs. 600     B) Rs. 620     C) Rs. 660      D) Rs. 680     E) Rs. 720
Sol: S.I. for 1 year = (900 − 840) = Rs.60
S.I. for 3 years = (60 × 3) = Rs.180.
Principal = (840 − 180) = Rs. 660.
                                                                   Ans: C

 

9. A sum fetched a total simple interest of Rs. 1600 at the rate of 20 p.c.p.a. in 4 years. What is the sum?
A) Rs.3000     B) Rs.2800     C) Rs.2600    D) Rs.2000     E) Rs.2500
Sol: Simple Interest

 

10. How much time will it take for an amount of Rs. 2400 to yield Rs. 3000 as interest at 10% per annum of simple interest?
A) 11 years     B) 12.5 years     C) 13 years     D) 14.5 years     E) 16 years
Sol: Simple Interest

 

11. Swetha took a loan of Rs.2400 with simple interest for as many years as the rate of interest. If she paid Rs.864 as interest at the
end of the loan period, what was the rate of interest?
A) 4%     B) 8%     C) 36%     D) 12%     E) 6%
Sol: Let rate = x% and time = x years.
Simple Interest

 

12. A sum of Rs.20000 amounts to Rs.24000 in 8 years at the rate of simple interest. What is the rate of interest?
A) 3%      B) 2.5%     C) 5%     D) 7%     E) 1.25%
Sol: S.I. = (24000 − 20000) = Rs.4000
Simple Interest

 

13. Hari took a loan from a bank at the rate of 20% p.a simple interest. After 4 years he had to pay Rs.8400 interest only for the
period. The principal amount borrowed by Hari was:
A) Rs. 21,000      B) Rs.10,500    C) Rs.36,000     D) Rs.9,500    E) Rs.8,000
Sol:
Simple Interest

 

14. What will be the ratio of simple interest earned by a certain amount at the same rate of interest for 10 years and that for 15 years?
A) 7 : 4     B) 5 : 3    C) 2 : 3    D) 4 : 3     E) 3 : 2
Sol: Let the principal be P and rate of interest be R%

 

15. A certain amount earns simple interest of Rs.2650 after 6 years. Had the interest been 5% more, how much more interest would it have earned?
A) Rs.400     B) Rs.500     C) Rs.600    D) Rs.700     E) Data inadequate
Sol: We need to know the S.I., principal and time to find the rate of interest in the first case.
Since the principal is not given, the data is inadequate.                                Ans: E

 

16. Rs.12200 was partly invested in Scheme A at 10% p.a compound interest (compounded annually) for 2 years and partly in
Scheme B at 10% p.a simple interest for 4 years. Both the schemes earn equal interests. How much was invested in Scheme A?
A) Rs.10,000    B) Rs.8,000    C) Rs.12,000     D) Rs.14,000     E) Rs.9,000
Sol: Let the amount invested in Scheme A is Rs. a.
Then, the amount invested in Scheme B be Rs. (12200 − a)
Now, according to the question,

 

Some more Questions

 

1. The Simple Interest accured on an amount of Rs.38,420 at the end of 4 years is Rs.7684. What is the rate of interest per year?
A) 10%      B) 12%      C) 5%     D) 16%        E) 7%

Sol: Given SI = 7684, T = 4 years, P = 38420

 

2. The interest received at 12% per annum Simple Interest after 5 years is Rs.840. What was the principal (in Rs.)?
A) Rs.1400     B) Rs.1700      C) Rs.2000     D) Rs.1900       E) Rs.2300

 

3. A sum of money becomes 6 times in 10 years. Find the 9 times of rate of interest?
A) 45%     B) 450%      C) 50%       D) 500%      E) 250%
Sol: formula:

 

4. A sum becomes 7 fold at 12% per annum. At what rate, the sum becomes 15 fold?
A) 20%      B) 24%      C) 28%      D) 32%      E) 34%

 

5. A sum of Rs.1000 amounts to Rs.1200 in 4 years at Simple Interest. If the interest rate is increased by 5%, it would amount to how much?
A) Rs.1000     B) Rs.2000     C) Rs.2600      D) Rs.1200      E) Rs.1400
Sol: P = 1000, A = 1200

 

6. At what rate percent per annum will a sum of money double in 24 years?

 

7. The Simple Interest on a sum of money at 14% per annum for 8 years is half the sum is:
A) Rs.2000    B) Rs.4000     C) Rs.8000    D) Rs.6000      E) Data insufficient

 

8. A sum of Rs.1600 was lent partly at 5% and partly at 10% per annum Simple Interest. The total interest received after 4 years was
Rs.400. The ratio of money lent at 5% to that lent at 10% is ......
A) 4 : 5     B) 2 : 3     C) 3 : 1      D) 6 : 7      E) 9 : 7

Sol: Using Allegation method

 

9. A certain sum of money amounts to 7/4 of itself in 12 years. What is the Simple Interest per annum?

A) 5.25%     B) 6.25%      C) 7.25%      D) 4.25%      E) 6.50%

 

10. Sushmitha deposited Rs.6400 which amounted 8000 after 4 years at SI. Had the interest been 1.25% more, she would get how much amount?
A) Rs.8320      B) Rs.8760      C) Rs.9230     D) Rs.9600      E) RS.8120
Sol: SI = 1600, P = 6400, T = 4 years

 

11. A man borrowed Rs.1000 for 3 years and Rs.1500 for 4 years at the same rate Simple Interest and required only Rs.1800 as interest.
What was the rate % p.a?
A) 20%     B) 30%     C) 10%     D) 15%     E) 7%
Sol: Rs.1000 for 3 years and Rs.1500 for 4 years

 

12. SI for a sum of Rs.1500 for 3 years is Rs.420 more than the SI for 1200 for the same duration. Find the rate of interest.
A) 15%     B) 20%     C) 25%     D) 30%      E) 10%
Sol: SI on 1500 − SI on 12000 = 420

 

13. The principal on which a Simple Interest of Rs.40 will be obtained after 6 months at the rate of 25/4% per annum is....
A) Rs.1280     B) Rs.1220     C) Rs.1240     D) Rs.1260      E) Rs.1290
Sol: Let principal = P

 

14. At what rate percent per annum simple interest will a sum of money becomes 4 times of itself in 4 years?
A) 45%     B) 65%      C) 50%       D) 60%      E) 75%
Sol: Amount = 4P; Time = 4 years
SI = 4P − P = 3P

 

15. A man buys a refrigerator at Rs.20000. He pays Rs.4000 at once and the rest after 2 years on which he is charged at Simple Interest at the rate of 20% per year. The total amount he pays for the refrigerator is....
A) Rs.20400     B) Rs.22400      C) Rs.24000     D) Rs.26800       E) Rs.32000
Sol: P = 20000 − 4000 = 16000
R = 20%, T = 2 years

 

16. What would be the Simple Interest obtained on an amount of Rs.46465 at the rate of 10% p.a after 6 years? (in Rs.)
A) 30961      B) 25462      C) 6849     D) 10824       E) 27879

 

17. If a sum of money amounts to Rs.14000 and Rs.16000 at the end of 3rd year and 4th year respectively a certain rate of Simple Interest, then the rate of interest is .....
A) 10%     B) 12.5%      C) 25%      D) 14%       E) 18%

Sol: SI for 1 year
= SI for 4 years − SI for 3 years
= 16000 − 14000
SI for 1 year = 2000
SI for 3 years = 2000 × 3 = 6000

 

18. Simple Interest on a sum after 4 years is 68/75 of th sum. The rate of interest per annum is ......

 

19. Two equal sums were lent at 8% and 10% SI respectively. The interest earned on the two loans add up to Rs.3600 for 4 years. The total sum lent out in .... (in Rs.)
A) 3000     B) 4000     C) 5000     D) 2500     E) 2000
Sol: Let Principle be x

 

Some More....

      * Interest is the additional money paid for the usage 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 same amount of money it 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, T is time and S.I. the simple interest, then

                        

Note: Simple interest is always calculated on principal. Therefore simple interest is equal for every period.

e.g: 1. What would be the simple interest obtained on an a amount of Rs. 6850 at the rate of 6 p.c.p.a. after 3 years?

(A) Rs. 2423     (B) Rs. 1233     (C) Rs. 1633     (D) Rs. 1525    (E) None of these

Sol: Here P = Rs. 6850,     T= 3 years and     R = 6%
           


         Hence answer is (B)

 

2. How long will it take for Rs. 1250 to become Rs. 1600 at 7% per annum simple interest?
       (A) 5 years            (B) 3 years          (C) 4 years         (D) 6 years     (E) None of these
Sol:        
             
               Hence Answer is (C)

 

3. What would be the amount on Rs. 8250 for 4 years at 15% per annum simple interest?

     (A) Rs. 13200    (B) Rs. 12300   (C) Rs. 10450     (D) Rs. 11200   (E) None of these

SOl:    
                


Shortcut: for one year, rate of interest is 15% and for 4 years it is 15×4 = 60% The Amount will become 160% If 100% Money = 8250,

Compound Interest:

    Interest which is calculated not only on the initial principal but also the accumulated interest of prior periods.

    If A is the amount, C.I. is the compound interest, P is the principal, R is the rate, and T

is the time, then  

 

 e.g: What is the compound interest accrued on an amount of Rs. 8000, at the rate of 6%
p.a. at the end of 2 years?
      (A) Rs.2545     (B) Rs.2,257.20     (C) Rs.2986   (D) Rs.2775.40    (E) None of these
Sol:         


               
Shortcut:  Amount = 106% of 106% 8000 =  8988.80
                         C.I. = 8988.80 - 8000 = Rs. 988.80
Note: 1. If the interest is paid half yearly, time is doubled and the rate is halved.
            2. If the interest is paid quarterly, time becomes 4 times and the rate becomes onefourth

 

 e.g: What is the interest accrued on Rs.12000 for one and half year at 4% p.a. compounded
half yearly?

Difference between Simple and Compound Interest

     Difference between Simple Interest and Compound Interest can be calculated by using formulae.

     There is no difference between Simple and Compound Interest for one year. For 2 years
                         

 
e.g: 1. What is the difference between Simple and Compound Interest for two years on Rs. 24000 at 7% rate?
Sol:      


                
                   = Rs. 117.60
2. On what sum does the difference between Simple and Compound Interest for 3 years at 5% rate will be Rs. 244?

Sol:        

 

Some other Models of Questions:

1. A sum of money will become Rs. 8060 in 4 years at 6% per annum simple interest. Find the sum.
Sol:        


           
Shortcut: For one year, rate of interest is 6% and for 4 years it is 4 × 6% = 24% Then the amount will become 124%
If 124% money is Rs. 8060, 100% money will be   × 8060 = Rs. 6500

 

2. Find the simple interest on Rs. 17500 at 7% per annum from August 5th to October 17th in the same year.

Sol: Time from August 5th to October 17th 

 =  26 days of August + 30 days of September and 17 days of October

 

3. A sum was put at simple interest at a certain rate for 2 years. Had it been put at 3% higher rate, it would have fetched Rs. 72 more. What is that sum?

Sol: Interest for 2 years is Rs. 72. For one year it is Rs. 36
3% interest money is Rs. 72, then 100% money  × 36 = Rs. 1200
                                                     Sum is Rs. 1200

 

4. A certain sum of money invested at compound interest doubles in 3 years. In how many years will it become 6 times itself?

Sol: Let the money be Rs. x It becomes Rs. 2x in 3 years As this is compound interest, 2x will be the principal for next period. Therefore, 2x will become 4x in next 3 years hence Rs. x will become 4x
       i.e. 4 times in 3 + 3 = 6 years


5. A man deposits Rs. 12600 in a bank at 5% annual interest. After 8 months he withdraws Rs. 5400 together with interest and after 4 months the remaining money. How much does he get as interest at the end of the year?

Sol: S.I. of Rs. 12600 for 8 months


                       
He withdrew Rs. 5400 together with interest, the remaining amount
                        = 12600 - 5400 = Rs. 7200                    

 
S.I. on Rs. 7200 at the rate of 5% for 4 months 


 Total interest = 420 + 120 = Rs. 540

Posted Date : 30-08-2022

గమనిక : ప్రతిభ.ఈనాడు.నెట్లో వచ్చే ప్రకటనలు అనేక దేశాల నుండి, వ్యాపారస్తులు లేదా వ్యక్తుల నుండి వివిధ పద్ధతులలో సేకరించబడతాయి. ఆయా ప్రకటనకర్తల ఉత్పత్తులు లేదా సేవల గురించి ఈనాడు యాజమాన్యానికీ, ఉద్యోగస్తులకూ ఎటువంటి అవగాహనా ఉండదు. కొన్ని ప్రకటనలు పాఠకుల అభిరుచిననుసరించి కృత్రిమ మేధస్సు సాంకేతికతతో పంపబడతాయి. ఏ ప్రకటనని అయినా పాఠకులు తగినంత జాగ్రత్త వహించి, ఉత్పత్తులు లేదా సేవల గురించి తగిన విచారణ చేసి, తగిన జాగ్రత్తలు తీసుకొని కొనుగోలు చేయాలి. ఉత్పత్తులు / సేవలపై ఈనాడు యాజమాన్యానికి ఎటువంటి నియంత్రణ ఉండదు. కనుక ఉత్పత్తులు లేదా సేవల నాణ్యత లేదా లోపాల విషయంలో ఈనాడు యాజమాన్యం ఎటువంటి బాధ్యత వహించదు. ఈ విషయంలో ఎటువంటి ఉత్తర ప్రత్యుత్తరాలకీ తావు లేదు. ఫిర్యాదులు తీసుకోబడవు.

 

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