1. A bank offers 5% compound interest calculated on half-yearly basis. A customer deposits Rs. 1600 each on 1st January and 1st July of a year. At the end of the year, the amount he would have gained by way of interest is:
A. Rs. 120
B. Rs. 121
C. Rs. 122
D. Rs. 123
2- The difference between simple and compound interests compounded annually on a certain sum of money for 2 years at 4% per annum is Re. 1. The sum (in Rs.) is:
A. 625
B. 630
C. 640
D. 650
3- There is 60% increase in an amount in 6 years at simple interest. What will be the compound interest of Rs. 12,000 after 3 years at the same rate?
A. Rs. 2160
B. Rs. 3120
C. Rs. 3972
D. Rs. 6240
E. None of these
4- What is the difference between the compound interests on Rs. 5000 for 1 years at 4% per annum compounded yearly and half-yearly?
A. Rs. 2.04
B. Rs. 3.06
C. Rs. 4.80
D. Rs. 8.30
5- The compound interest on Rs. 30,000 at 7% per annum is Rs. 4347. The period (in years) is:
A. 2
B. 2 1/2
C. 3
D. 4
6. What will be the compound interest on a sum of Rs. 25,000 after 3 years at the rate of 12 p.c.p.a.?
A. Rs. 9000.30
B. Rs. 9720
C. Rs. 10123.20
D. Rs. 10483.20
E. None of these
7. At what rate of compound interest per annum will a sum of Rs. 1200 become Rs. 1348.32 in 2 years?
A. 6%
B. 6.5%
C. 7%
D. 7.5%
8. The least number of complete years in which a sum of money put out at 20% compound interest will be more than doubled is:
A. 3
B. 4
C. 5
D. 6
9. Albert invested an amount of Rs. 8000 in a fixed deposit scheme for 2 years at compound interest rate 5 p.c.p.a. How much amount will Albert get on maturity of the fixed deposit?
A. Rs. 8600
B. Rs. 8620
C. Rs. 8820
D. None of these
10. The effective annual rate of interest corresponding to a nominal rate of 6% per annum payable half-yearly is:
A. 6.06%
B. 6.07%
C. 6.08%
D. 6.09%
11. Simple interest on a certain sum of money for 3 years at 8% per annum is half the compound interest on Rs. 4000 for 2 years at 10% per annum. The sum placed on simple interest is:
A. Rs. 1550
B. Rs. 1650
C. Rs. 1750
D. Rs. 2000
12. If the simple interest on a sum of money for 2 years at 5% per annum is Rs. 50, what is the compound interest on the same at the same rate and for the same time?
A. Rs. 51.25
B. Rs. 52
C. Rs. 54.25
D. Rs. 60
13. The difference between simple interest and compound on Rs. 1200 for one year at 10% per annum reckoned half-yearly is:
A. Rs. 2.50
B. Rs. 3
C. Rs. 3.75
D. Rs. 4
E. None of these
14. The difference between compound interest and simple interest on an amount of Rs. 15,000 for 2 years is Rs. 96. What is the rate of interest per annum?
A. 8
B. 10
C. 12
D. Cannot be determined
E. None of these
15. The compound interest on a certain sum for 2 years at 10% per annum is Rs. 525. The simple interest on the same sum for double the time at half the rate percent per annum is:
A. Rs. 400
B. Rs. 500
C. Rs. 600
D. Rs. 800
1. एक बैंक अर्ध-वार्षिक आधार पर गणना किए गए 5% चक्रवृद्धि ब्याज की पेशकश करता है। एक ग्राहक रुपये जमा करता है। 1600 प्रत्येक को 1 जनवरी और 1 जुलाई को। वर्ष के अंत में, उसे ब्याज के रूप में प्राप्त होने वाली राशि है:
ए. रु. 120
बी रु. 121
सी. रु. 122
डी. रु. 123
2- एक निश्चित राशि पर 2 वर्ष के लिए 4% प्रति वर्ष की दर से वार्षिक चक्रवृद्धि ब्याज और साधारण ब्याज के बीच का अंतर रु है। 1. योग (रुपये में) है:
ए. 625
बी 630
सी 640
डी 650
3- साधारण ब्याज पर 6 वर्षों में एक राशि में 60% की वृद्धि होती है। रुपये का चक्रवृद्धि ब्याज क्या होगा? 12,000 3 साल बाद उसी दर पर?
ए. रु. 2160
बी रु. 3120
सी. रु. 3972
डी. रु. 6240
इनमें से कोई नहीं
4- रुपये पर चक्रवृद्धि ब्याज के बीच क्या अंतर है। 5000 1 वर्ष के लिए 4% प्रति वर्ष की दर से वार्षिक और अर्ध-वार्षिक रूप से संयोजित?
ए. रु. 2.04
बी रु. 3.06
सी. रु. 4.80
डी. रु. 8.30
5- रुपये पर चक्रवृद्धि ब्याज। 30,000 7% प्रति वर्ष की दर से रु. 4347. अवधि (वर्षों में) है:
ए 2
बी 2 1/2
सी. 3
डी. 4
6. रुपये की राशि पर चक्रवृद्धि ब्याज क्या होगा? 25,000 3 साल बाद 12 प्रतिशत प्रति वर्ष की दर से?
ए. रु. 9000.30
बी रु. 9720
सी. रु. 10123.20
डी. रु. 10483.20
इनमें से कोई नहीं
7. प्रति वर्ष चक्रवृद्धि ब्याज की किस दर पर राशि रु. 1200 रु. 2 साल में 1348.32?
ए 6%
बी 6.5%
सी. 7%
डी 7.5%
8. कम से कम पूर्ण वर्षों की संख्या जिसमें 20% चक्रवृद्धि ब्याज पर रखी गई राशि दोगुनी से अधिक हो जाएगी:
ए 3
बी 4
सी. 5
डी. 6
9. अल्बर्ट ने रुपये की राशि का निवेश किया। 8000 एक सावधि जमा योजना में 2 साल के लिए चक्रवृद्धि ब्याज दर 5 प्रतिशत प्रति वर्ष पर। सावधि जमा की परिपक्वता पर अल्बर्ट को कितनी राशि मिलेगी?
ए. रु. 8600
बी रु. 8620
सी. रु. 8820
D. इनमें से कोई नहीं
10. अर्ध-वार्षिक देय 6% प्रति वर्ष की मामूली दर के अनुरूप प्रभावी वार्षिक ब्याज दर है:
ए 6.06%
बी 6.07%
सी 6.08%
डी 6.09%
11. एक निश्चित राशि पर 3 वर्षों के लिए 8% प्रति वर्ष की दर से साधारण ब्याज रुपये पर चक्रवृद्धि ब्याज का आधा है। 4000 2 साल के लिए 10% प्रति वर्ष। साधारण ब्याज पर रखी गई राशि है:
ए. रु. 1550
बी रु. 1650
सी. रु. 1750
डी. रु. 2000
12. यदि किसी धनराशि पर 5% वार्षिक की दर से 2 वर्ष का साधारण ब्याज रु. 50, समान दर पर और समान समय के लिए उसी पर चक्रवृद्धि ब्याज कितना है?
ए. रु. 51.25
बी रु. 52
सी. रु. 54.25
डी. रु. 60
13. रुपये पर साधारण ब्याज और चक्रवृद्धि के बीच का अंतर। एक वर्ष के लिए 100% प्रति वर्ष की दर से 1200 अर्धवार्षिक माना जाता है:
ए. रु. 2.50
बी रु. 3
सी. रु. 3.75
डी. रु. 4
इनमें से कोई नहीं
14. रुपये की राशि पर चक्रवृद्धि ब्याज और साधारण ब्याज के बीच का अंतर। 2 साल के लिए 15,000 रुपये है। 96. प्रति वर्ष ब्याज दर क्या है?
ए 8
बी 10
सी. 12
D. निर्धारित नहीं किया जा सकता
इनमें से कोई नहीं
15. एक निश्चित राशि पर 2 वर्ष के लिए 10% प्रतिवर्ष की दर से चक्रवृद्धि ब्याज रु. 525. समान राशि पर प्रति वर्ष की आधी दर से दुगुने समय पर साधारण ब्याज है:
ए. रु. 400
बी रु. 500
सी. रु. 600
डी. रु. 800
1. Find the compound interest (CI) on Rs. 12,600 for 2 years at 10% per annum compounded annually.
Solution:
Given,
Principal (P) = Rs. 12,600
Rate (R) = 10
Number of years (n) = 2
A = P[1 +(R/100)]n
= 12600[1 + (10/100)]2
= 12600[1 + (1/10)]2
= 12600 [(10 + 1)/10]2
= 12600 × (11/10) × (11/10)
= 126 × 121
= 15246
Total amount, A = Rs. 15,246
Compound interest (CI) = A – P
= Rs. 15,246 – Rs. 12,600
= Rs. 2646
2. At what rate of compound interest per annum, a sum of Rs. 1200 becomes Rs. 1348.32 in 2 years?
Solution:
Let R% be the rate of interest per annum.
Given,
Principal (P) = Rs. 1200
Total amount after 2 years (A) = Rs. 1348.32
n = 2
We know that,
A = P[1 + (R/100)]n
Rs. 1348.32 = Rs. 1200[1 + (R/100)]2
1348.32/1200 = [1 + (R/100)]2
[1 + (R/100)]2 = 134832/120000
[1 + (R/100)]2 = 2809/2500
[1 + (R/100)]2 = (53/50)2
1 + (R/100) = 53/50
R/100 = (53/50) – 1
R/100 = (53 – 50)/50
R = 300/50
R = 6
Hence, the rate of interest is 6%.
Amount, when interest is compounded half-yearly, is
A = P[1 + (R/200)]2n
Here,
R/200 = half-yearly rate
2n = the number of half years
3. A TV was bought for Rs. 21,000. The value of the TV was depreciated by 5% per annum. Find the value of the TV after 3 years. (Depreciation means the reduction of value due to use and age of the item)
Solution:
Principal (P) = Rs. 21,000
Rate of depreciation (R) = 5%
n = 3
Using the formula of CI for depreciation,
A = P[1 – (R/100)]n
A = Rs. 21,000[1 (5/100)]3
= Rs. 21,000[1 – (1/20)]3
= Rs. 21,000[(20 – 1)/20]3
= Rs. 21,000 × (19/20) × (19/20) × (19/20)
= Rs. 18,004.875
Therefore, the value of the TV after 3 years = Rs. 18,004.875.
4. Find the compound interest on Rs 48,000 for one year at 8% per annum when compounded half-yearly.
Solution:
Given,
Principal (P) = Rs 48,000
Rate (R) = 8% p.a.
Time (n) = 1 year
Also, the interest is compounded half-yearly.
So, A = P[1 + (R/200)]2n
= Rs. 48000[1 + (8/200)]2(1)
= Rs. 48000[1 + (1/25)]2
= Rs. 48000[(25 + 1)/25]2
= Rs. 48,000 × (26/25) × (26/25)
= Rs. 76.8 × 26 × 26
= Rs 51,916.80
Therefore, the compound interest = A – P
= Rs (519,16.80 – 48,000)
= Rs 3,916.80
5. Find the compound interest on Rs. 8000 at 15% per annum for 2 years 4 months, compounded annually.
Solution:
Given,
Principal (P) = Rs. 8000
Rate of interest (R) = 15% p.a
Time (n) = 2 years 4 months
4 months = 4/12 years = 1/3 years
So,
A = P[1 + (R/100)]n
= Rs. 8000 [1 + (15/100)]2 [1 + (1/3) × (15/100)]
= Rs. 8000 [1 + (3/20)]2 [1 + (3/20 × 3)]
= Rs. 8000 [(20 + 3)/20]2 [(20 + 1)/20]
= Rs. 8000 × (23/20) × (23/20) × (21/20)
= Rs. 11,109
Therefore, the compound interest = A – P = Rs. 11,109 – Rs. 8000 = Rs. 3109
6. If principal = Rs 1,00,000. rate of interest = 10% compounded half-yearly. Find
(i) Interest for 6 months.
(ii) Amount after 6 months.
(iii) Interest for the next 6 months.
(iv) Amount after one year.
Solution:
Given,
P = Rs 1,00,000
R = 10%
(i) A = P[1 + (R/200)]2n
Here, 2n is the number of half years.
Let us find the interest compounded half-yearly for 6 months, i.e., one half year.
So, A = Rs. 1,00,000 [1 + (10/200)]1
= Rs. 1,00,000 [(20 + 1)/20]
= Rs. 1,00,000 × 21/20
= Rs. 1,05,000
Compounded interest for 6 months = Rs. 1,05,000 – Rs. 1,00,000 = Rs. 5000
(ii) Amount after 6 months = Rs. 1,05,000
(iii) To find the interest for the next 6 months, we should consider the principal amount as Rs. 1,05,000.
Thus, A = Rs. 1,05,000 [1 + (10/200)]1
= Rs. 1,05,000 × (21/20)
= Rs. 1,10,250
Compound interest for next 6 months = Rs. 1,10,250 – Rs. 1,05,000 = Rs. 5250
(iv) Amount after one year = Rs. 1,10,250
7. The population of a place increased to 54,000 in 2003 at a rate of 5% per annum.
(i) Find the population in 2001.
(ii) What would be its population in 2005?
Solution:
(i) Let P be the population in the year 2001.
Thus, population in the year 2003 = A = 54000 (given)
R = 5%
Also, n = 2
A = P[1 + (R/100)]n
54000 = P[1 + (5/100)]2
54000 = P[1 + (1/20)]2
54000 = P × [(20 + 1)/20]2
54000 = P × (21/20) × (21/20)
P = 54000 × (20/21) × (20/21)
P = 48979.6
The population in 2001 = 48980 (approx.)
(ii) Given that the population in the year 2003 = P = 54000
R = 5%
n = 2
A = P[1 + (R/100)]n
= 54000[1 + (5/100)]2
= 54000[1 + (1/20)]2
= 54000 × [(20 + 1)/20]2
= 54000 × (21/20) × (21/20)
= 59535
Therefore, the population in 2005 = 59535
Amount, when interest is compounded quarterly, is
A = P[1 + (R/400)]4n
Here,
R/400 = Quarterly rate
4n = The number of quarters
1. रुपये पर चक्रवृद्धि ब्याज (CI) ज्ञात कीजिए। 12,600 2 साल के लिए 10% प्रतिवर्ष की दर से सालाना चक्रवृद्धि।
समाधान:
दिया गया,
प्रिंसिपल (पी) = रु। 12,600
दर (आर) = 10
वर्षों की संख्या (एन) = 2
ए = पी[1 +(आर/100)]एन
= 12600 [1 + (10/100)] 2
= 12600 [1 + (1/10)] 2
= 12600 [(10 + 1)/10] 2
= 12600 × (11/10) × (11/10)
= 126 × 121
= 15246
कुल राशि, ए = रु। 15,246
चक्रवृद्धि ब्याज (CI) = A - P
= रु. 15,246 - रु। 12,600
= रु. 2646
2. प्रति वर्ष चक्रवृद्धि ब्याज की किस दर पर, रु. 1200 रुपये हो जाता है। 2 साल में 1348.32?
समाधान:
मान लीजिए कि R% प्रतिवर्ष ब्याज की दर है।
दिया गया,
प्रिंसिपल (पी) = रु। 1200
2 साल बाद कुल राशि (ए) = रु। 1348.32
एन = 2
हम जानते हैं कि,
ए = पी[1 + (आर/100)]एन
रु. 1348.32 = रु. 1200 [1 + (आर/100)] 2
1348.32/1200 = [1 + (आर/100)]2
[1 + (आर/100)]2 = 134832/122000
[1 + (आर/100)]2 = 2809/2500
[1 + (आर/100)]2 = (53/50)2
1 + (आर/100) = 53/50
आर/100 = (53/50) - 1
आर/100 = (53 - 50)/50
आर = 300/50
आर = 6
अत: ब्याज की दर 6% है।
राशि, जब ब्याज अर्धवार्षिक रूप से संयोजित किया जाता है, है
ए = पी[1 + (आर/200)]2एन
यहां,
आर/200 = अर्धवार्षिक दर
2n = आधे साल की संख्या
3. एक टीवी रुपये में खरीदा गया था। 21,000 टीवी के मूल्य में 5% प्रति वर्ष की कमी की गई थी। 3 वर्ष बाद टीवी का मूल्य ज्ञात कीजिए। (मूल्यह्रास का अर्थ है वस्तु के उपयोग और उम्र के कारण मूल्य में कमी)
समाधान:
प्रिंसिपल (पी) = रु। 21,000
मूल्यह्रास की दर (आर) = 5%
एन = 3
मूल्यह्रास के लिए CI के सूत्र का उपयोग करते हुए,
ए = पी[1 - (आर/100)]एन
ए = रु। 21,000 [1 (5/100)]3
= रु. 21,000 [1 - (1/20)]3
= रु. 21,000[(20 – 1)/20]3
= रु. 21,000 × (19/20) × (19/20) × (19/20)
= रु. 18,004.875
अत: 3 वर्ष बाद टीवी का मूल्य = रु. 18,004.875.
4. अर्ध-वार्षिक रूप से संयोजित होने पर 8% प्रति वर्ष की दर से एक वर्ष के लिए 48,000 रुपये पर चक्रवृद्धि ब्याज ज्ञात कीजिए।
समाधान:
दिया गया,
मूलधन (पी) = रुपये 48,000
दर (आर) = 8% प्रति वर्ष
समय (एन) = 1 वर्ष
साथ ही, ब्याज अर्ध-वार्षिक रूप से संयोजित होता है।
तो, ए = पी[1 + (आर/200)]2एन
= रु. 48000[1 + (8/200)]2(1)
= रु. 48000 [1 + (1/25)] 2
= रु. 48000 [(25 + 1)/25] 2
= रु. 48,000 × (26/25) × (26/25)
= रु. 76.8 × 26 × 26
= 51,916.80 रुपये
अत: चक्रवृद्धि ब्याज = A – P
= रुपये (519,16.80 - 48,000)
= रु 3,916.80
5. रुपये पर चक्रवृद्धि ब्याज ज्ञात कीजिए। 8000 15% प्रति वर्ष की दर से 2 साल 4 महीने के लिए, सालाना चक्रवृद्धि।
समाधान:
दिया गया,
प्रिंसिपल (पी) = रु। 8000
ब्याज दर (आर) = 15% प्रति वर्ष
समय (एन) = 2 साल 4 महीने
4 महीने = 4/12 साल = 1/3 साल
इसलिए,
ए = पी[1 + (आर/100)]एन
= रु. 8000 [1 + (15/100)]2 [1 + (1/3) × (15/100)]
= रु. 8000 [1 + (3/20)]2 [1 + (3/20 × 3)]
= रु. 8000 [(20 + 3)/20]2 [(20 + 1)/20]
= रु. 8000 × (23/20) × (23/20) × (21/20)
= रु. 11,109
अत: चक्रवृद्धि ब्याज = A - P = रु. 11,109 - रु। 8000 = रु. 3109
6. यदि मूलधन = 1,00,000 रु. ब्याज दर = 10% छमाही चक्रवृद्धि। पाना
(i) 6 महीने के लिए ब्याज।
(ii) 6 महीने के बाद की राशि।
(iii) अगले 6 महीनों के लिए ब्याज।
(iv) एक वर्ष के बाद की राशि।
समाधान:
दिया गया,
पी = रुपये 1,00,000
आर = 10%
(i) ए = पी[1 + (आर/200)]2एन
यहाँ, 2n आधे वर्षों की संख्या है।
आइए हम 6 महीने, यानी एक छमाही के लिए अर्ध-वार्षिक रूप से चक्रवृद्धि ब्याज ज्ञात करें।
तो, ए = रु। 1,00,000 [1 + (10/200)]1
= रु. 1,00,000 [(20 + 1)/20]
= रु. 1,00,000 × 21/20
= रु. 1,05,000
6 महीने के लिए चक्रवृद्धि ब्याज = रु. 1,05,000 - रु। 1,00,000 = रु. 5000
(ii) 6 महीने के बाद की राशि = रु। 1,05,000
(iii) अगले 6 महीनों के लिए ब्याज का पता लगाने के लिए, हमें मूल राशि को रुपये के रूप में मानना चाहिए। 1,05,000.
इस प्रकार, ए = रु। 1,05,000 [1 + (10/200)]1
= रु. 1,05,000 × (21/20)
= रु. 1,10,250
अगले 6 महीनों के लिए चक्रवृद्धि ब्याज = रु. 1,10,250 - रु। 1,05,000 = रु. 5250
(iv) एक वर्ष के बाद की राशि = रु। 1,10,250
7. एक जगह की जनसंख्या 2003 में 5% प्रति वर्ष की दर से बढ़कर 54,000 हो गई।
(i) 2001 में जनसंख्या ज्ञात कीजिए।
(ii) 2005 में इसकी जनसंख्या कितनी होगी?
समाधान:
(i) मान लीजिए P वर्ष 2001 में जनसंख्या है।
अत: वर्ष 2003 में जनसंख्या = A = 54000 (दिया गया)
आर = 5%
साथ ही, n = 2
ए = पी[1 + (आर/100)]एन
54000 = पी [1 + (5/100)] 2
54000 = पी[1 + (1/20)]2
54000 = पी × [(20 + 1)/20]2
54000 = पी × (21/20) × (21/20)
पी = 54000 × (20/21) × (20/21)
पी = 48979.6
2001 में जनसंख्या = 48980 (लगभग)
(ii) दिया गया है कि वर्ष 2003 में जनसंख्या = P = 54000
आर = 5%
एन = 2
ए = पी[1 + (आर/100)]एन
= 54000 [1 + (5/100)] 2
= 54000 [1 + (1/20)]2
= 54000 × [(20 + 1)/20]2
= 54000 × (21/20) × (21/20)
= 59535
अतः 2005 में जनसंख्या = 59535
राशि, जब ब्याज त्रैमासिक रूप से संयोजित होता है, है
ए = पी[1 + (आर/400)]4एन
यहां,
आर/400 = त्रैमासिक दर
4n = तिमाहियों की संख्या
8. What is the difference between the compound interests on Rs. 5000 for 1 ½ year at 4% per annum compounded yearly and half-yearly?
Solution:
Given,
P = Rs. 5000
R = 4%
Time (n) = 1 ½ years
When the interest is compounded yearly,
A = P[1 + (R/100)]n
= Rs. 5000 [1 + (4/100)] [1 + (1/2 × 4/100)]
= Rs. 5000 [1 + (1/25)] [1 + (1/50)]
= Rs. 5000 [(25 + 1)/25] [(50 + 1)/50]
= Rs. 5000 × (26/25) × (51/50)
= Rs. 5304
CI = A – P = Rs. 5304 – Rs. 5000 = Rs. 304
When the interest is compounded half-yearly,
n = 1 ½ years = 3 half-years
A = P[1 + (R/200)]2n
Here, 2n = 3
A = Rs. 5000 [1 + (4/200)]3
= Rs. 5000 [1 + (1/50)]3
= Rs. 5000 [(50 + 1)/50]3
= Rs. 5000 × (51/50) × (51/50) × (51/50)
= Rs. 5306.04
CI = A – P = Rs. 5306.04 – Rs. 5000 = Rs. 306.04
Difference between compound interest = Rs. 306.04 – Rs. 304 = Rs. 2.04
9. The population of a town decreased every year due to migration, poverty and unemployment. The present population of the town is 6,31,680. Last year the migration was 4%, and the year before last, it was 6%. What was the population two years ago?
Solution:
Given,
The present population of the town (A) = 631680
Last year migration rate was 4%, and the year before, the previous migration rate was 6%.
Let P be the population of a town, two years ago.
Thus, R1 = 4%
R2 = 6%
According to the given situation, the total population is:
A = P[1 – (R1/100)] [1 – (R2/100)]
631680 = P [1 – (4/100)] [1 – (6/100)]
631680 = P [1 – (1/25)] [1 – (3/50)]
631680 = P[(25 – 1)/25] [(50 – 3)/50]
631680 = P × (24/25) × (47/50)
P = 631680 × (25/24) × (50/47)
P = 700000
Therefore, the population of the town, two years ago = 700000
10. Find the amount and the compound interest on Rs. 1,00,000 compounded quarterly for 9 months at the rate of 4% per annum.
Solution:
Given,
P = Rs. 1,00,000
R = 4%
Time = 9 months
A = P[1 + (R/400)]4n
Here, R/400 is the quarterly interest rate.
4n = 9 months = 3 quarters
So, A = Rs. 1,00,000 [1 + (4/400)]3
= Rs. 1,00,000 [1 + (1/100)]3
= Rs. 1,00,000 [(100 + 1)/100]3
= Rs. 1,00,000 × (101/100) × (101/100) × (101/100)
= Rs. 103030.10
8. रुपये पर चक्रवृद्धि ब्याज के बीच क्या अंतर है? 5000 1 1/2 वर्ष के लिए 4% प्रति वर्ष की दर से वार्षिक और अर्ध-वार्षिक रूप से संयोजित?
समाधान:
दिया गया,
पी = रु। 5000
आर = 4%
समय (एन) = 1 ½ वर्ष
जब ब्याज वार्षिक रूप से संयोजित होता है,
ए = पी[1 + (आर/100)]एन
= रु. 5000 [1 + (4/100)] [1 + (1/2 × 4/100)]
= रु. 5000 [1 + (1/25)] [1 + (1/50)]
= रु. 5000 [(25 + 1)/25] [(50 + 1)/50]
= रु. 5000 × (26/25) × (51/50)
= रु. 5304
सीआई = ए - पी = रु। 5304 - रु। 5000 = रु। 304
जब ब्याज अर्धवार्षिक संयोजित होता है,
n = 1 1/2 वर्ष = 3 अर्ध-वर्ष
ए = पी[1 + (आर/200)]2एन
यहाँ, 2n = 3
ए = रु। 5000 [1 + (4/200)]3
= रु. 5000 [1 + (1/50)]3
= रु. 5000 [(50 + 1)/50]3
= रु. 5000 × (51/50) × (51/50) × (51/50)
= रु. 5306.04
सीआई = ए - पी = रु। 5306.04 - रु। 5000 = रु। 306.04
चक्रवृद्धि ब्याज में अंतर = रु. 306.04 - रु। 304 = रु. 2.04
9. प्रवास, गरीबी और बेरोजगारी के कारण हर साल एक शहर की जनसंख्या में कमी आई है। शहर की वर्तमान जनसंख्या 6,31,680 है। पिछले साल प्रवासन 4% था, और पिछले साल यह 6% था। दो वर्ष पूर्व जनसंख्या कितनी थी?
समाधान:
दिया गया,
शहर की वर्तमान जनसंख्या (ए) = 631680
पिछले साल प्रवासन दर 4% थी, और एक साल पहले, पिछली प्रवासन दर 6% थी।
मान लीजिए P दो वर्ष पहले एक कस्बे की जनसंख्या है।
अत: R1 = 4%
R2 = 6%
दी गई स्थिति के अनुसार, कुल जनसंख्या है:
ए = पी[1 - (आर1/100)] [1 - (आर2/100)]
631680 = पी [1 - (4/100)] [1 - (6/100)]
631680 = पी [1 - (1/25)] [1 - (3/50)]
631680 = पी[(25 - 1)/25] [(50 - 3)/50]
631680 = पी × (24/25) × (47/50)
पी = 631680 × (25/24) × (50/47)
पी = 700000
अत: दो वर्ष पूर्व शहर की जनसंख्या = 700000
10. रुपये पर राशि और चक्रवृद्धि ब्याज का पता लगाएं। 1,00,000 4% प्रति वर्ष की दर से 9 महीने के लिए तिमाही चक्रवृद्धि।
समाधान:
दिया गया,
पी = रु। 1,00,000
आर = 4%
समय = 9 महीने
ए = पी[1 + (आर/400)]4एन
यहां, R/400 तिमाही ब्याज दर है।
4एन = 9 महीने = 3 तिमाही
तो, ए = रु। 1,00,000 [1 + (4/400)]3
= रु. 1,00,000 [1 + (1/100)]3
= रु. 1,00,000 [(100 + 1)/100]3
= रु. 1,00,000 × (101/100) × (101/100) × (101/100)
= रु. 103030.10
- The principle that amounts to Rs. 4913 in 3 years at 6 1/4 % per annum C.I. compounded annually, is?
A. Rs. 3096
B. Rs. 4076
C. Rs. 4085
D. Rs. 4096 - Find the Compound Interest on Rs.8000 at 5% per annum for 3 years when C.I is reckoned yearly?
A. Rs. 1,185
B. Rs. 1,261
C. Rs. 1,346
D. Rs. 1,440 - The difference between simple interest and C.I. at the same rate for Rs.5000 for 2 years in Rs.72. The rate of interest is?
A. 6%
B. 8%
C. 10%
D. 12% - The difference between compound and simple interest on a certain sum of money for 3 years at 6 2/3% p.a is Rs.184. Find the sum?
A. Rs.12,000
B. Rs.13,500
C. Rs.14,200
D. Rs.17,400
Answer: D. Rs. 4096
Explanation: According to the formula,
Principle = [4913 / (1 + 25/ (4 * 100))3]
=> 4913 * 16/17 * 16/17 * 16/17 = Rs. 4096
Answer: B. Rs. 1,261
Explanation: A = 8000(21/20)^3 = 9261
Now, 9261 - 8000 = Rs. 1,261
Answer: D. 12%
Explanation: 5000 = 72(100/R)^2
5 R^2 = 720 => R = 12
Answer: B. Rs.13,500
Explanation: P = (184*10^6) / [6 2/3 * 6 2/3 *(300*6 2/3)]
P = 13500
- A sum of money is put out at compound interest for 2 years at 20%. It would fetch Rs.482 more if the interest were payable half-yearly, then it were pay able yearly. Find the sum.
A. Rs.1,000
B. Rs.1,250
C. Rs.2,000
D. Rs.4,000 - The difference between the compound interest compounded annually and simple interest for 2 years at 20% per annum is Rs.144. Find the principal?
A. Rs.3,000
B. Rs.3,300
C. Rs.3,600
D. Rs.3,900 - Find the amount on Rs.8000 in 9 months at 20% per annum, if the interest being compounded quarterly?
A. Rs.9,021
B. Rs.9,162
C. Rs.9,261
D. Rs.9,621
Answer: C. Rs.2,000
Explanation: P(11/10)^4 - P(6/5)^2 = 482
P = 2000
Answer: C. Rs.3,600
Explanation: P = 144(100/5)^2 => P = 3600
Answer: C. Rs.9,261
Explanation: A = 8000(21/20)^3 = 9261
- Every year an amount increases by 1/8th of itself. How much will it be after two years if its present value is Rs.64000?
A. Rs.61,000
B. Rs.65,000
C. Rs.71,000
D. Rs.81,000 - Indu gave Bindu Rs.1250 on compound interest for 2 years at 4% per annum. How much loss would Indu has suffered had she given it to Bindu for 2 years at 4% per annum simple interest?
A. Rs.10
B. Rs.5
C. Rs.3
D. Rs.2 - How much more would Rs.20000 fetch, after two years, if it is put at 20% p.a. compound interest payable half yearly than if is put at 20% p.a. compound interest payable yearly?
A. Rs.424
B. Rs.482
C. Rs.512
D. Rs.842
Answer: D. Rs.81,000
Explanation: 64000* 9/8 * 9/8 = 81000
Answer: D. Rs.2
Explanation: 1250 = D(100/4)^2
D = 2
Answer: B. Rs.482
Explanation: 20000(11/10)^4 - 20000(6/5)^2 = 482
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