is called the Amount (A).
A = P + I
Simple Interest (S.I.)
When interest is charged on the original sum (Principal) borrowed throughout the loan period, it is called simple interest.
Example:
Find the interest to be owed on a sum of Rs 2500 at 5% p.a. for a period of 3 years
Solution:
Example:
An amount given on S.I. becomes three times of itself in 8 years Find the rate of interest charged.
Solution:
A = P + I ⇒ 3P = P + I ⇒ I = 2P And also, S. I. =
⇒
⇒
Compound Interest (C.I.)
When the interest that becomes due is added to the principal and the interest for the next period is calculated on the new principal, then such scheme of interest is called compound interest.
Second year's principal = First year's principal + First year's interest.
When interest is payable annually.
When interest is payable half–yearly.
When rates are different for different years, say R1, R2, R3 per cent for the first, second and third year respectively then
Amount =
In case the time is a fraction of a year, say years, then
Amount = Example:
Find the C.I. on a principal of Rs 1200, for two years when rate of interest for first years is 2% and for the second year is 5%.
Solution:
A =
= 1285.2
4 Simple & Compound
Interest
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⇒ C.I = A – P = 1285.2 – 1200 = Rs 85.2 Population Formula:
The population of a town is P and annual rate of increase of population is R%, then the population of the town n years is given by .
If the rate of decrease of population is R% the population after n years is given by: . This is also called the Depreciation formula.
Example:
If the annual increase in the population of a town is 4% and the present population is 16625 what will be its population after 3 years (Approximate).
Solution:
Population after 3 years
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1. Ramu invests Rs.8,000 in two banks. Bank 1 offers 5% simple interest per annum and Bank 2 offers 9% simple interest per annum. Interest for three years from these two investments come out to be Rs. 1440. Then what is the amount invested at 5 % per annum?
a. Rs 2,000 b. Rs 3,000 c. Rs 5,000 d. Rs 6,000
2. Population of certain cancer bacteria grows at a rate of 20 % per annum and this cancer can be cured if the bacteria are detected when grown to 1, 00,000. If a person starts feeling the symptoms of these bacteria when he has 50,000 bacteria, at what time a person has to start his treatment from the time he first notices the symptoms of these bacteria?
a. 4 years
b. Less than 4 years c. More than 4 years d. None of the above
3. If the difference between SI and CI on a con-stant principal is Rs 305 for a period of 3 years and rate of interest in both the cases is 5 % per annum then what was the principal amount invested in both cases. for 3 years comes out to be Rs 3000 and simple interest on the same sum of money in a differ-ent scheme of SI for 2 years comes out to be Rs 2250. Find the amount of money invested?
Assume rate of interest per annum in both the cases to be single digit integers.
a. Rs 12000 b. Rs 12500 c. Rs 13000 d. Rs 13500
6. Ramu had to invest some money for three years He had two options open with him. In the first option, bank was offering a Simple Interest of 10 % and in the second option, bank was offering compound interest of 8 % per annum compounded annually. Which of the two options is a better deal?
a. First Option b. Second Option
c. Both the options are equally good d. None of the above
7. If ratio of SI and CI for two years is 20:21 then what is the rate of interest offered in both the cases? Assume principal money invested and rate of interest offered is same in both the cases.
a. 5 % b. 10 %
c. 20 % d. Cannot be determined 8. Ramu started investing in a recurring deposit
wherein he need to pay an amount of Rs 10,000 on every 1st of January for 5 years and he will get the total amount due at the end of 5th year.
If bank pays a compound interest of 10 per cent per annum then how much money should Ramu get at the end of 5th year?
a. 59,267 b. 67,157 c. 74,124 d. 81,134
9. Ramu purchased a TV set for Rs 50,000 and decided to pay the total amount in 5 equal monthly instalments. If rate of interest charged by the bank was 2.5% per month then what will be the approximate value of that monthly instalment? Assume that the first monthly in-stallment is to be paid at the time of purchase of TV.
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Com-pound Interest for 2 years on a certain sum of money @ 8% per annum is Rs 8,000. What was the Principal amount invested?a. 10,00,000 b. 12,50,000 c. 15,00,000 d. 17,50,000
11. Value of machinery depreciates at a rate of 10%
every year. If value of three year old machinery is Rs 10935 then what was the price of the machinery when it was purchased?
a. Rs 12,000 b. Rs 15,000 c. Rs 18,000 d. Rs 20,000
12. I invested some amount of money at certain rate of interest at SI and I realized that my money has increased to four times in four years. In how many years, it will increase to 16 times?
a. 12 years b. 16 years c. 20 years d. 24 years
13. At certain rate of compound interest, it was realized that amount at the end of 3 years will be Rs 5,750 and amount at the end of 6 years
money triples in 6 years. In how many years it will increase to 27 times the original principal invested?
a. 54 years b. 27 years c. 18 years d. 45 years
15. Spirit evaporates at a rate of 10 % every min-ute if left open in air. One fine day, Ramu by mistake left the spirit jar open in air. After how much time, volume of the jar will be less than or equal to 60 % of the original volume?
a. 4 min b. 5 min c. 6 min d. 7 min
16. Chaman has purchased a bungalow in Jhum-ritalaiya. Cost of the land on which the flat is built is Rs 81,00,000 and price of the building is Rs 1,21,00,000. Price of the land appreciates
at a rate of 10% per annum whereas the cost of the building depreciates at a rate of 10 % per annum. After how many years, cost of the land and building will be equal?
a. 1 year b. 2 years c. 3 years d. 4 years
17. What will be the approximate compound inter-est on Rs 20,000 for nine months at 20 % per annum compounded quarterly?
a. Rs 3,000 b. Rs 3,125 c. Rs 3,150 d. Rs 3,500
18. Ramu invested Rs 10,000 in a scheme of com-pound interest wherein rate of interest for first year was 5%, for next couple of years it was 10% and then onwards it was 20%. What will be the net amount that Ramu will receive at the end of 5 years if money was compounded an-nually?
a. Rs 18,295.2 b. Rs 17,465.2 c. Rs 18,467.8 d. Rs 18,269.8
19. Population of a town increases at a rate of 15%
per annum. What was the population of this town two years back if the current population of the town is 29,09,500?
a. 20,00,000 b. 21,00,000 c. 22,00,000 d. 23,00,000
20. Billu borrowed Rs 10,000 partly from Kallu and partly from Lallu. He agreed to repay the money to Kallu at simple interest of 5% per of the machine is Rs 8,000.
a. Rs 5,120 b. Rs 6,858 c. Rs 9,452 d. Rs 6,772
22. Current population of Jhumritalaiya is 1,50,000.
Male population of Jhumritalaiya increases at a rate of 5% per annum and female
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tion increases at a rate of 10 % per annum. If the population of Jhumritalaiya is expected to be 1, 75, 050 two years hence, then what percentage of the current population is male?
a. 40% b. 60%
c. 90% d. 10%
23. Compound Interest on a certain sum of money for two years at 10 % per annum is Rs 1,680.
Find the simple interest on the same sum of money at the same rate?
a. Rs 1,550 b. Rs 1,665 c. Rs 1,600 d. Rs 1,650
24. The simple interest on a certain sum of money will be Rs 200 after 4 years. For the next 4 years if the principal is trebled, then what will be the additional interest in next four year because of the increase in principal?
a. 300 b. 450
c. 400 d. 500
25. A sum was given at simple interest at a certain rate for 3 years. It would have fetched Rs 90 more had it been charged interest at 3% higher rate. Find the Sum?
a. 1100 b. 1000
c. 1200 d. 500
26. A sum of Rs 800 amounts to Rs 960 in 4 years at simple interest. What will be the amount if the rate of interest is increased by 4%?
a. 1088 b. 1188 c. 188 d. 1888
27. If a certain sum of money becomes double at simple interest in 10 years, what would be the rate of simple interest per annum?
a. 12 b. 10
c. 11 d. 12.5
28. A sum of money becomes of itself in 5 years. Find the rate of simple interest charged?
a. 20 b. 30
30. The population of Dalsing Sarai is 300000. If the annual birth rate is 6% and death rate is year at the rate of 10% per annum compounded quarterly.
a. 1300 b. 1100 c. 13288 d. 1200
32. If the annual increase in the population of a town is 5% and the present population be 92610000, what was the population three years ago?
a. 8 × 107 b. 8 × 106 c. 8 × 105 d. 7 × 107
33. The simple interest on a sum is ¼th of the principal and the rate of interest per annum was equal to the number of years, find the rate per cent.
a. 6 b. 9
c. 5 d. 8
34. Niraj lent Rs 1200 to Nitin for 2 years, and Rs 1500 to Raghunath for 4 years and received Rs 420 as interest from both of them. Find the rate of interest if rate of interest in both the cases is same is calculated as Simple Interest.
a. 5 b. 6 annum. Find the simple interest and the amount.
a. 80 b. 100
c. 200 d. 50
37. In what time, at simple interest will sum of money treble itself at 20%.
a. 12 b. 10
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c. 15 d. 20
38. The value of a machinery decreases every year at the rate of 15% on its value at the beginning of that year. If its present value be Rs 4913, what was its value 3 years ago?
a. 7000 b. 9000 c. 8000 d. 4500
39. A certain sum of money amounts to Rs 960 in 2 years and to Rs 1200 in 5 years at certain rate of Simple Interest. Find the rate of interest per annum? for 7 years, find the total interest accured?
a. 900 b. 400 parts in such a way that the interest on one part at 5% for 6 years is equal to that on another mode of interset to be Simple Interest.
a. 1800 b. 1640
per annum. Find the value of the car after three years.
a. 59852 b. 54872 c. 60452 d. 52785
50. A man invests Rs 5000 for 3 years at 5% p.a.
compound interest reckoned yearly. Income tax at the rate of 20% on the interest earned is deducted at the end of each year. Find the amount at the end of the third year.
a. Rs 5624.32 b. Rs 5630.50 c. Rs 5788.125 d. Rs 5627.20
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