Simple and Compound Interest

Simple & Compound Interest – 50 Questions with Answers (Hindi + English)

1. What is Simple Interest?
(सरल ब्याज क्या होता है?)

Simple Interest (SI) is the interest calculated only on the principal amount for a certain period at a given rate. Formula: SI = (P × R × T) / 100 where P = Principal, R = Rate of interest, T = Time in years.

सरल ब्याज केवल मूलधन पर एक निश्चित अवधि के लिए निर्धारित दर से गणना किया जाता है। सूत्र: SI = (P × R × T) / 100 जहाँ P = मूलधन, R = ब्याज दर, T = समय (वर्षों में)।

2. Calculate the Simple Interest on ₹10,000 at 5% per annum for 3 years.
(₹10,000 पर 5% वार्षिक दर से 3 वर्षों के लिए सरल ब्याज ज्ञात करें।)

Given: P = 10,000, R = 5%, T = 3 years
SI = (10,000 × 5 × 3) / 100 = ₹1,500.

दिया गया: P = 10,000, R = 5%, T = 3 वर्ष
SI = (10,000 × 5 × 3) / 100 = ₹1,500।

3. What is Compound Interest?
(चक्रवृद्धि ब्याज क्या होता है?)

Compound Interest (CI) is the interest calculated on the principal amount plus the interest earned in previous periods. Formula: CI = A – P, where A = P(1 + R/100)^T.

चक्रवृद्धि ब्याज वह ब्याज है जो मूलधन और पिछले वर्षों के ब्याज दोनों पर लगाया जाता है। सूत्र: CI = A – P, जहाँ A = P(1 + R/100)^T।

4. Calculate the Compound Interest on ₹5,000 at 10% per annum for 2 years.
(₹5,000 पर 10% वार्षिक दर से 2 वर्षों के लिए चक्रवृद्धि ब्याज ज्ञात करें।)

P = 5,000, R = 10%, T = 2 years
A = 5,000 × (1 + 10/100)^2 = 5,000 × 1.21 = ₹6,050
CI = A – P = 6,050 – 5,000 = ₹1,050.

P = 5,000, R = 10%, T = 2 वर्ष
A = 5,000 × (1 + 10/100)^2 = 5,000 × 1.21 = ₹6,050
CI = A – P = 6,050 – 5,000 = ₹1,050।

5. If the Simple Interest on a sum for 3 years at 4% per annum is ₹360, find the principal.
(यदि किसी राशि पर 3 वर्षों के लिए 4% वार्षिक सरल ब्याज ₹360 है, तो मूलधन ज्ञात करें।)

SI = 360, R = 4%, T = 3 years
P = (SI × 100) / (R × T) = (360 × 100) / (4 × 3) = ₹3,000.

SI = 360, R = 4%, T = 3 वर्ष
P = (SI × 100) / (R × T) = (360 × 100) / (4 × 3) = ₹3,000।

6. Find the amount after 2 years on ₹8,000 at 6% simple interest.
(₹8,000 पर 6% सरल ब्याज के साथ 2 वर्षों के बाद राशि ज्ञात करें।)

P = 8,000, R = 6%, T = 2 years
SI = (8,000 × 6 × 2)/100 = ₹960
Amount = Principal + SI = 8,000 + 960 = ₹8,960.

P = 8,000, R = 6%, T = 2 वर्ष
SI = (8,000 × 6 × 2)/100 = ₹960
राशि = मूलधन + सरल ब्याज = 8,000 + 960 = ₹8,960।

7. Calculate compound interest for ₹2,000 at 5% per annum for 3 years compounded annually.
(₹2,000 पर 5% वार्षिक दर से 3 वर्षों के लिए वार्षिक चक्रवृद्धि ब्याज ज्ञात करें।)

P = 2,000, R = 5%, T = 3 years
A = 2,000 × (1 + 5/100)^3 = 2,000 × 1.157625 = ₹2,315.25
CI = 2,315.25 – 2,000 = ₹315.25.

P = 2,000, R = 5%, T = 3 वर्ष
A = 2,000 × (1 + 5/100)^3 = 2,000 × 1.157625 = ₹2,315.25
चक्रवृद्धि ब्याज = 2,315.25 – 2,000 = ₹315.25।

8. What is the difference between Simple Interest and Compound Interest?
(सरल ब्याज और चक्रवृद्धि ब्याज में क्या अंतर है?)

Simple Interest is calculated only on the principal amount.
Compound Interest is calculated on principal plus accumulated interest.
CI ≥ SI for same principal, rate, and time.

सरल ब्याज केवल मूलधन पर गणना किया जाता है।
चक्रवृद्धि ब्याज मूलधन और जमा ब्याज दोनों पर गणना किया जाता है।
एक ही मूलधन, दर और समय के लिए चक्रवृद्धि ब्याज सरल ब्याज से अधिक या बराबर होता है।

9. If the compound interest on ₹1,200 for 2 years at 5% per annum is ₹123, find the principal.
(₹1,200 पर 2 वर्षों के लिए 5% वार्षिक चक्रवृद्धि ब्याज ₹123 है, तो मूलधन ज्ञात करें।)

Given CI = ₹123, R = 5%, T = 2 years.
Amount A = Principal + CI = 1,200 + 123 = ₹1,323.
Using formula A = P(1 + R/100)^T =>
1,323 = P × (1.05)^2 = P × 1.1025
P = 1,323 / 1.1025 ≈ ₹1,200.

चक्रवृद्धि ब्याज = ₹123, R = 5%, T = 2 वर्ष।
राशि A = मूलधन + CI = 1,200 + 123 = ₹1,323।
सूत्र A = P(1 + R/100)^T अनुसार:
1,323 = P × (1.05)^2 = P × 1.1025
P = 1,323 / 1.1025 ≈ ₹1,200।

10. Find the amount on ₹7,000 at 8% simple interest for 4 years.
(₹7,000 पर 8% सरल ब्याज के लिए 4 वर्षों के बाद राशि ज्ञात करें।)

P = 7,000, R = 8%, T = 4 years
SI = (7,000 × 8 × 4)/100 = ₹2,240
Amount = Principal + SI = 7,000 + 2,240 = ₹9,240.

P = 7,000, R = 8%, T = 4 वर्ष
सरल ब्याज = (7,000 × 8 × 4)/100 = ₹2,240
राशि = मूलधन + सरल ब्याज = 7,000 + 2,240 = ₹9,240।

11. A sum of ₹12,000 is lent at 7% per annum simple interest. Find the interest for 5 years.
₹12,000 राशि 7% वार्षिक सरल ब्याज पर उधार दी गई है। 5 वर्षों के लिए ब्याज ज्ञात करें।

SI = (12,000 × 7 × 5) / 100 = ₹4,200.

सरल ब्याज = (12,000 × 7 × 5) / 100 = ₹4,200।

12. Find the compound interest on ₹3,000 at 6% per annum for 2 years compounded yearly.
₹3,000 पर 6% वार्षिक चक्रवृद्धि ब्याज के लिए 2 वर्षों के लिए वार्षिक चक्रवृद्धि ब्याज ज्ञात करें।

A = 3,000 × (1 + 6/100)^2 = 3,000 × 1.1236 = ₹3,370.80
CI = 3,370.80 – 3,000 = ₹370.80.

राशि = 3,000 × (1 + 6/100)^2 = 3,000 × 1.1236 = ₹3,370.80
चक्रवृद्धि ब्याज = 3,370.80 – 3,000 = ₹370.80।

13. If the simple interest on a sum for 4 years is ₹1,200 at 5% per annum, find the principal.
यदि किसी राशि पर 4 वर्षों के लिए 5% वार्षिक सरल ब्याज ₹1,200 है, तो मूलधन ज्ञात करें।

P = (SI × 100) / (R × T) = (1,200 × 100) / (5 × 4) = ₹6,000.

P = (सरल ब्याज × 100) / (दर × समय) = (1,200 × 100) / (5 × 4) = ₹6,000।

14. What will be the amount on ₹9,000 at 8% simple interest for 3 years?
₹9,000 पर 8% सरल ब्याज के लिए 3 वर्षों के बाद राशि क्या होगी?

SI = (9,000 × 8 × 3) / 100 = ₹2,160.
Amount = 9,000 + 2,160 = ₹11,160.

सरल ब्याज = (9,000 × 8 × 3) / 100 = ₹2,160।
राशि = 9,000 + 2,160 = ₹11,160।

15. Calculate the compound interest on ₹1,500 for 3 years at 4% per annum compounded annually.
₹1,500 पर 4% वार्षिक चक्रवृद्धि ब्याज के लिए 3 वर्षों के लिए वार्षिक चक्रवृद्धि ब्याज ज्ञात करें।

A = 1,500 × (1 + 4/100)^3 = 1,500 × 1.124864 = ₹1,687.30
CI = 1,687.30 – 1,500 = ₹187.30.

राशि = 1,500 × (1 + 4/100)^3 = 1,500 × 1.124864 = ₹1,687.30
चक्रवृद्धि ब्याज = 1,687.30 – 1,500 = ₹187.30।

16. The simple interest on a sum is ₹750 for 5 years at 5% per annum. Find the principal.
किसी राशि पर 5 वर्षों के लिए 5% सरल ब्याज ₹750 है। मूलधन ज्ञात करें।

P = (750 × 100) / (5 × 5) = ₹3,000.

P = (750 × 100) / (5 × 5) = ₹3,000।

17. Find the compound interest on ₹2,500 at 5% per annum for 4 years compounded annually.
₹2,500 पर 5% वार्षिक चक्रवृद्धि ब्याज के लिए 4 वर्षों के लिए वार्षिक चक्रवृद्धि ब्याज ज्ञात करें।

A = 2,500 × (1 + 5/100)^4 = 2,500 × 1.215506 = ₹3,038.77
CI = 3,038.77 – 2,500 = ₹538.77.

राशि = 2,500 × (1 + 5/100)^4 = 2,500 × 1.215506 = ₹3,038.77
चक्रवृद्धि ब्याज = 3,038.77 – 2,500 = ₹538.77।

18. A sum amounts to ₹1,764 in 2 years at 8% simple interest. Find the principal.
8% सरल ब्याज दर पर 2 वर्षों में राशि ₹1,764 हुई है। मूलधन ज्ञात करें।

Let P = principal.
SI = Amount – Principal = 1,764 – P
SI = (P × 8 × 2)/100 = 0.16P
So, 1,764 – P = 0.16P => 1,764 = 1.16P => P = 1,764 / 1.16 = ₹1,520.

मान लें P = मूलधन।
सरल ब्याज = राशि – मूलधन = 1,764 – P
सरल ब्याज = (P × 8 × 2)/100 = 0.16P
अतः, 1,764 – P = 0.16P => 1,764 = 1.16P => P = 1,764 / 1.16 = ₹1,520।

19. What will be the compound interest on ₹5,000 at 10% per annum for 1 year compounded half-yearly?
₹5,000 पर 10% वार्षिक चक्रवृद्धि ब्याज के लिए 1 वर्ष के लिए अर्धवार्षिक चक्रवृद्धि ब्याज ज्ञात करें।

Rate per half year = 10% / 2 = 5%
Number of periods = 2
A = 5,000 × (1 + 5/100)^2 = 5,000 × 1.1025 = ₹5,512.50
CI = 5,512.50 – 5,000 = ₹512.50.

प्रत्येक छह महीने की दर = 10% / 2 = 5%
अवधि = 2
राशि = 5,000 × (1 + 5/100)^2 = 5,000 × 1.1025 = ₹5,512.50
चक्रवृद्धि ब्याज = 5,512.50 – 5,000 = ₹512.50।

20. Find the simple interest on ₹15,000 at 9% per annum for 6 months.
₹15,000 पर 9% सरल ब्याज के लिए 6 महीने का ब्याज ज्ञात करें।

T = 6 months = 0.5 years
SI = (15,000 × 9 × 0.5)/100 = ₹675.

समय = 6 महीने = 0.5 वर्ष
सरल ब्याज = (15,000 × 9 × 0.5)/100 = ₹675।

21. The compound interest on ₹10,000 for 2 years at 6% per annum compounded annually is ₹1,236. Find the amount.
₹10,000 पर 6% वार्षिक चक्रवृद्धि ब्याज के लिए 2 वर्षों में चक्रवृद्धि ब्याज ₹1,236 है। राशि ज्ञात करें।

Amount = Principal + CI = 10,000 + 1,236 = ₹11,236.

राशि = मूलधन + चक्रवृद्धि ब्याज = 10,000 + 1,236 = ₹11,236।

22. A sum of ₹5,000 amounts to ₹6,105 in 3 years. Find the rate of interest if simple interest is applied.
₹5,000 राशि 3 वर्षों में ₹6,105 हो जाती है। सरल ब्याज दर ज्ञात करें।

SI = 6,105 – 5,000 = ₹1,105
P = 5,000, T = 3 years
R = (SI × 100) / (P × T) = (1,105 × 100) / (5,000 × 3) = 7.37%.

सरल ब्याज = 6,105 – 5,000 = ₹1,105
P = 5,000, T = 3 वर्ष
दर = (सरल ब्याज × 100) / (मूलधन × समय) = (1,105 × 100) / (5,000 × 3) = 7.37%।

23. Find the amount after 3 years on ₹7,000 at 12% per annum compound interest compounded yearly.
₹7,000 पर 12% वार्षिक चक्रवृद्धि ब्याज के लिए 3 वर्षों के बाद राशि ज्ञात करें।

A = 7,000 × (1 + 12/100)^3 = 7,000 × 1.404928 = ₹9,834.50.

राशि = 7,000 × (1 + 12/100)^3 = 7,000 × 1.404928 = ₹9,834.50।

24. How much time will it take for a sum of ₹4,000 to amount to ₹5,120 at 8% per annum simple interest?
₹4,000 राशि 8% वार्षिक सरल ब्याज पर ₹5,120 बनने में कितना समय लगेगा?

SI = 5,120 – 4,000 = ₹1,120
P = 4,000, R = 8%
T = (SI × 100) / (P × R) = (1,120 × 100) / (4,000 × 8) = 3.5 years.

सरल ब्याज = 5,120 – 4,000 = ₹1,120
P = 4,000, R = 8%
समय = (सरल ब्याज × 100) / (मूलधन × दर) = (1,120 × 100) / (4,000 × 8) = 3.5 वर्ष।

25. Find the compound interest on ₹6,000 at 5% per annum for 2 years compounded half yearly.
₹6,000 पर 5% वार्षिक चक्रवृद्धि ब्याज के लिए 2 वर्षों के लिए अर्धवार्षिक चक्रवृद्धि ब्याज ज्ञात करें।

Rate per half year = 5/2 = 2.5%
Number of periods = 2 × 2 = 4
A = 6,000 × (1 + 2.5/100)^4 = 6,000 × 1.10381289 = ₹6,622.88
CI = 6,622.88 – 6,000 = ₹622.88.

अर्धवार्षिक दर = 5/2 = 2.5%
अवधि = 2 × 2 = 4
राशि = 6,000 × (1 + 2.5/100)^4 = 6,000 × 1.10381289 = ₹6,622.88
चक्रवृद्धि ब्याज = 6,622.88 – 6,000 = ₹622.88।

26. A sum of ₹10,000 is invested at compound interest for 3 years and it amounts to ₹12,650. Find the rate of interest per annum.
₹10,000 की राशि 3 वर्षों के लिए चक्रवृद्धि ब्याज पर निवेश की गई और राशि ₹12,650 हो गई। वार्षिक ब्याज दर ज्ञात करें।

A = P (1 + R/100)^3 = 12,650
12,650/10,000 = (1 + R/100)^3 => 1.265 = (1 + R/100)^3
Cube root of 1.265 ≈ 1.083
1 + R/100 = 1.083 => R = 8.3%.

राशि = मूलधन × (1 + दर/100)^3 = 12,650
12,650/10,000 = (1 + दर/100)^3 => 1.265 = (1 + दर/100)^3
1.265 का घनमूल ≈ 1.083
1 + दर/100 = 1.083 => दर = 8.3%।

27. If the compound interest on ₹8,000 at 4% per annum for 2 years is ₹665.60, find the frequency of compounding.
₹8,000 पर 4% वार्षिक चक्रवृद्धि ब्याज के लिए 2 वर्षों में चक्रवृद्धि ब्याज ₹665.60 है। चक्रवृद्धि की आवृत्ति ज्ञात करें।

Let’s check for annual compounding:
A = 8,000 × (1 + 4/100)^2 = 8,000 × 1.0816 = 8,652.80
CI = 8,652.80 – 8,000 = 652.80 (Not 665.60)
Try semi-annual:
Rate per half year = 2%, n = 4
A = 8,000 × (1 + 2/100)^4 = 8,000 × 1.082432 = ₹8,659.46
CI = 659.46 (Still not 665.60)
Try quarterly:
Rate per quarter = 1%, n=8
A= 8,000 × (1 + 1/100)^8 = 8,000 × 1.0828567= 8,662.85
CI = 662.85 (Closer)
For monthly:
Rate per month = 4/12=0.3333%, n=24
A = 8,000 × (1 + 0.003333)^24 ≈ 8,000 × 1.083 = 8,664
CI ≈ 664 (Very close)
So frequency approximately monthly.

वार्षिक चक्रवृद्धि पर जांच करें:
राशि = 8,000 × (1 + 4/100)^2 = 8,000 × 1.0816 = 8,652.80
चक्रवृद्धि ब्याज = 652.80 (₹665.60 नहीं)
अर्धवार्षिक प्रयास करें:
अर्धवार्षिक दर = 2%, n = 4
राशि = 8,000 × (1 + 2/100)^4 = 8,000 × 1.082432 = ₹8,659.46
चक्रवृद्धि ब्याज = 659.46 (₹665.60 नहीं)
त्रैमासिक प्रयास करें:
त्रैमासिक दर = 1%, n=8
राशि= 8,000 × (1 + 1/100)^8 = 8,000 × 1.082857 = 8,662.85
चक्रवृद्धि ब्याज = 662.85 (करीब)
मासिक प्रयास करें:
मासिक दर = 4/12=0.3333%, n=24
राशि ≈ 8,000 × 1.083 = 8,664
चक्रवृद्धि ब्याज ≈ 664 (बहुत करीब)
अतः आवृत्ति लगभग मासिक है।

28. Find the compound interest on ₹5,000 for 2 years at 6% per annum compounded annually.
₹5,000 की राशि पर 6% वार्षिक चक्रवृद्धि ब्याज 2 वर्षों के लिए ज्ञात करें।

A = 5,000 × (1 + 6/100)^2 = 5,000 × 1.1236 = ₹5,618
CI = 5,618 – 5,000 = ₹618.

राशि = 5,000 × (1 + 6/100)^2 = 5,000 × 1.1236 = ₹5,618
चक्रवृद्धि ब्याज = 5,618 – 5,000 = ₹618।

29. A sum amounts to ₹15,000 in 3 years at 5% per annum compound interest. Find the sum.
5% वार्षिक चक्रवृद्धि ब्याज दर पर 3 वर्षों में राशि ₹15,000 हो जाती है। मूलधन ज्ञात करें।

A = P (1 + 5/100)^3 = 15,000
P = 15,000 / (1.157625) = ₹12,948.72

राशि = मूलधन × (1 + 5/100)^3 = 15,000
मूलधन = 15,000 / 1.157625 = ₹12,948.72

30. Find the compound interest on ₹7,500 for 1 year at 8% per annum compounded half-yearly.
₹7,500 पर 8% वार्षिक दर से अर्धवार्षिक चक्रवृद्धि ब्याज 1 वर्ष के लिए ज्ञात करें।

Rate per half year = 8/2 = 4%
Number of periods = 2 × 1 = 2
A = 7,500 × (1 + 4/100)^2 = 7,500 × 1.0816 = ₹8,112
CI = 8,112 – 7,500 = ₹612.

अर्धवार्षिक दर = 8/2 = 4%
अवधि = 2 × 1 = 2
राशि = 7,500 × (1 + 4/100)^2 = 7,500 × 1.0816 = ₹8,112
चक्रवृद्धि ब्याज = 8,112 – 7,500 = ₹612।

31. If the compound interest on ₹9,000 for 2 years is ₹1,036.80, find the rate of interest per annum.
₹9,000 पर 2 वर्षों के लिए चक्रवृद्धि ब्याज ₹1,036.80 है। वार्षिक ब्याज दर ज्ञात करें।

A = 9,000 + 1,036.80 = ₹10,036.80
10,036.80 = 9,000 × (1 + R/100)^2
(1 + R/100)^2 = 10,036.80 / 9,000 = 1.1152
1 + R/100 = √1.1152 = 1.056
R = 5.6%.

राशि = 9,000 + 1,036.80 = ₹10,036.80
10,036.80 = 9,000 × (1 + दर/100)^2
(1 + दर/100)^2 = 10,036.80 / 9,000 = 1.1152
1 + दर/100 = √1.1152 = 1.056
दर = 5.6%।

32. A sum of ₹4,000 is invested at compound interest at 10% per annum. Find the amount after 2 years.
₹4,000 चक्रवृद्धि ब्याज पर 10% वार्षिक दर से निवेश किया गया है। 2 वर्षों के बाद राशि ज्ञात करें।

A = 4,000 × (1 + 10/100)^2 = 4,000 × 1.21 = ₹4,840.

राशि = 4,000 × (1 + 10/100)^2 = 4,000 × 1.21 = ₹4,840।

33. Find the compound interest on ₹12,000 for 3 years at 4% per annum compounded annually.
₹12,000 पर 4% वार्षिक दर से 3 वर्षों के लिए चक्रवृद्धि ब्याज ज्ञात करें।

A = 12,000 × (1 + 4/100)^3 = 12,000 × 1.124864 = ₹13,498.37
CI = 13,498.37 – 12,000 = ₹1,498.37.

राशि = 12,000 × (1 + 4/100)^3 = 12,000 × 1.124864 = ₹13,498.37
चक्रवृद्धि ब्याज = 13,498.37 – 12,000 = ₹1,498.37।

34. The compound interest on a sum for 2 years at 8% per annum is ₹1,728. Find the sum.
8% वार्षिक दर पर 2 वर्षों के लिए चक्रवृद्धि ब्याज ₹1,728 है। मूलधन ज्ञात करें।

Let sum = P
A = P + 1,728 = P (1 + 8/100)^2 = P × 1.1664
P + 1,728 = 1.1664 P
1,728 = 0.1664 P
P = 1,728 / 0.1664 = ₹10,385.42.

मान लें मूलधन = P
राशि = P + 1,728 = P × (1 + 8/100)^2 = P × 1.1664
P + 1,728 = 1.1664 P
1,728 = 0.1664 P
P = 1,728 / 0.1664 = ₹10,385.42।

35. A sum of ₹7,200 amounts to ₹8,467.20 in 2 years at compound interest. Find the rate of interest.
₹7,200 राशि 2 वर्षों में चक्रवृद्धि ब्याज पर ₹8,467.20 हो जाती है। ब्याज दर ज्ञात करें।

A = 8,467.20, P = 7,200, n = 2
8,467.20 = 7,200 × (1 + R/100)^2
(1 + R/100)^2 = 8,467.20 / 7,200 = 1.176
1 + R/100 = √1.176 = 1.084
R = 8.4%.

राशि = 8,467.20, मूलधन = 7,200, अवधि = 2 वर्ष
8,467.20 = 7,200 × (1 + दर/100)^2
(1 + दर/100)^2 = 8,467.20 / 7,200 = 1.176
1 + दर/100 = √1.176 = 1.084
दर = 8.4%।

36. Find the amount on ₹10,000 after 2 years at 12% per annum compounded quarterly.
₹10,000 पर 12% वार्षिक दर से त्रैमासिक चक्रवृद्धि ब्याज 2 वर्षों के बाद राशि ज्ञात करें।

Rate per quarter = 12/4 = 3%
Number of quarters = 2 × 4 = 8
A = 10,000 × (1 + 3/100)^8 = 10,000 × 1.26677 = ₹12,667.70.

त्रैमासिक दर = 12/4 = 3%
त्रैमासिक की संख्या = 2 × 4 = 8
राशि = 10,000 × (1 + 3/100)^8 = 10,000 × 1.26677 = ₹12,667.70।

37. A sum of ₹6,000 is invested at compound interest and amounts to ₹7,020 in 2 years. Find the rate of interest.
₹6,000 चक्रवृद्धि ब्याज पर निवेशित है और 2 वर्षों में ₹7,020 हो जाती है। ब्याज दर ज्ञात करें।

A = 7,020, P = 6,000, n = 2
7,020 = 6,000 × (1 + R/100)^2
(1 + R/100)^2 = 7,020 / 6,000 = 1.17
1 + R/100 = √1.17 = 1.0815
R = 8.15%.

राशि = 7,020, मूलधन = 6,000, अवधि = 2 वर्ष
7,020 = 6,000 × (1 + दर/100)^2
(1 + दर/100)^2 = 7,020 / 6,000 = 1.17
1 + दर/100 = √1.17 = 1.0815
दर = 8.15%।

38. Find the compound interest on ₹9,000 for 3 years at 7% per annum compounded annually.
₹9,000 पर 7% वार्षिक दर से 3 वर्षों के लिए चक्रवृद्धि ब्याज ज्ञात करें।

A = 9,000 × (1 + 7/100)^3 = 9,000 × 1.225043 = ₹11,025.39
CI = 11,025.39 – 9,000 = ₹2,025.39.

राशि = 9,000 × (1 + 7/100)^3 = 9,000 × 1.225043 = ₹11,025.39
चक्रवृद्धि ब्याज = 11,025.39 – 9,000 = ₹2,025.39।

39. The compound interest on a sum of money for 2 years at 10% per annum is ₹1,210. Find the sum.
10% वार्षिक दर पर 2 वर्षों के लिए चक्रवृद्धि ब्याज ₹1,210 है। मूलधन ज्ञात करें।

Let sum = P
Amount = P + 1,210 = P (1 + 10/100)^2 = P × 1.21
P + 1,210 = 1.21 P
1,210 = 0.21 P
P = 1,210 / 0.21 = ₹5,761.90.

मान लें मूलधन = P
राशि = P + 1,210 = P × (1 + 10/100)^2 = P × 1.21
P + 1,210 = 1.21 P
1,210 = 0.21 P
P = 1,210 / 0.21 = ₹5,761.90।

40. Find the amount and compound interest on ₹8,000 for 3 years at 6% per annum compounded half-yearly.
₹8,000 पर 6% वार्षिक दर से अर्धवार्षिक चक्रवृद्धि ब्याज 3 वर्षों के लिए राशि और ब्याज ज्ञात करें।

Rate per half year = 6/2 = 3%
Number of periods = 2 × 3 = 6
A = 8,000 × (1 + 3/100)^6 = 8,000 × 1.19405 = ₹9,552.40
CI = 9,552.40 – 8,000 = ₹1,552.40.

अर्धवार्षिक दर = 6/2 = 3%
अवधि = 2 × 3 = 6
राशि = 8,000 × (1 + 3/100)^6 = 8,000 × 1.19405 = ₹9,552.40
चक्रवृद्धि ब्याज = 9,552.40 – 8,000 = ₹1,552.40।

41. A sum of ₹15,000 amounts to ₹18,450 in 2 years at compound interest. Find the rate of interest.
₹15,000 राशि 2 वर्षों में चक्रवृद्धि ब्याज पर ₹18,450 हो जाती है। ब्याज दर ज्ञात करें।

A = 18,450, P = 15,000, n = 2
18,450 = 15,000 × (1 + R/100)^2
(1 + R/100)^2 = 18,450 / 15,000 = 1.23
1 + R/100 = √1.23 = 1.109
R = 10.9%.

राशि = 18,450, मूलधन = 15,000, अवधि = 2 वर्ष
18,450 = 15,000 × (1 + दर/100)^2
(1 + दर/100)^2 = 18,450 / 15,000 = 1.23
1 + दर/100 = √1.23 = 1.109
दर = 10.9%।

42. Find the compound interest on ₹5,500 for 2 years at 5% per annum compounded quarterly.
₹5,500 पर 5% वार्षिक दर से त्रैमासिक चक्रवृद्धि ब्याज 2 वर्षों के लिए ज्ञात करें।

Rate per quarter = 5/4 = 1.25%
Number of quarters = 2 × 4 = 8
A = 5,500 × (1 + 1.25/100)^8 = 5,500 × 1.104486 = ₹6,074.67
CI = 6,074.67 – 5,500 = ₹574.67.

त्रैमासिक दर = 5/4 = 1.25%
त्रैमासिक की संख्या = 2 × 4 = 8
राशि = 5,500 × (1 + 1.25/100)^8 = 5,500 × 1.104486 = ₹6,074.67
चक्रवृद्धि ब्याज = 6,074.67 – 5,500 = ₹574.67।

43. Find the amount on ₹20,000 after 1 year at 9% per annum compounded half-yearly.
₹20,000 पर 9% वार्षिक दर से अर्धवार्षिक चक्रवृद्धि ब्याज 1 वर्ष के बाद राशि ज्ञात करें।

Rate per half year = 9/2 = 4.5%
Number of half years = 2
A = 20,000 × (1 + 4.5/100)^2 = 20,000 × 1.092 = ₹21,840.

अर्धवार्षिक दर = 9/2 = 4.5%
अवधि = 2
राशि = 20,000 × (1 + 4.5/100)^2 = 20,000 × 1.092 = ₹21,840।

44. A sum of ₹8,500 amounts to ₹9,870 in 2 years at compound interest. Find the rate of interest.
₹8,500 राशि 2 वर्षों में चक्रवृद्धि ब्याज पर ₹9,870 हो जाती है। ब्याज दर ज्ञात करें।

A = 9,870, P = 8,500, n = 2
9,870 = 8,500 × (1 + R/100)^2
(1 + R/100)^2 = 9,870 / 8,500 = 1.161
1 + R/100 = √1.161 = 1.078
R = 7.8%.

राशि = 9,870, मूलधन = 8,500, अवधि = 2 वर्ष
9,870 = 8,500 × (1 + दर/100)^2
(1 + दर/100)^2 = 9,870 / 8,500 = 1.161
1 + दर/100 = √1.161 = 1.078
दर = 7.8%।

45. Find the compound interest on ₹6,500 for 3 years at 6% per annum compounded annually.
₹6,500 पर 6% वार्षिक दर से 3 वर्षों के लिए चक्रवृद्धि ब्याज ज्ञात करें।

A = 6,500 × (1 + 6/100)^3 = 6,500 × 1.191016 = ₹7,741.60
CI = 7,741.60 – 6,500 = ₹1,241.60.

राशि = 6,500 × (1 + 6/100)^3 = 6,500 × 1.191016 = ₹7,741.60
चक्रवृद्धि ब्याज = 7,741.60 – 6,500 = ₹1,241.60।

46. The compound interest on ₹10,000 for 2 years at 5% per annum is ₹1,025. Find the amount.
₹10,000 पर 5% वार्षिक दर से 2 वर्षों के लिए चक्रवृद्धि ब्याज ₹1,025 है। राशि ज्ञात करें।

Amount = Principal + CI = 10,000 + 1,025 = ₹11,025.

राशि = मूलधन + चक्रवृद्धि ब्याज = 10,000 + 1,025 = ₹11,025।

47. Find the compound interest on ₹7,000 for 2 years at 4% per annum compounded annually.
₹7,000 पर 4% वार्षिक दर से 2 वर्षों के लिए चक्रवृद्धि ब्याज ज्ञात करें।

A = 7,000 × (1 + 4/100)^2 = 7,000 × 1.0816 = ₹7,571.20
CI = 7,571.20 – 7,000 = ₹571.20.

राशि = 7,000 × (1 + 4/100)^2 = 7,000 × 1.0816 = ₹7,571.20
चक्रवृद्धि ब्याज = 7,571.20 – 7,000 = ₹571.20।

48. A sum of ₹5,000 amounts to ₹6,103 in 2 years at compound interest. Find the rate of interest.
₹5,000 राशि 2 वर्षों में चक्रवृद्धि ब्याज पर ₹6,103 हो जाती है। ब्याज दर ज्ञात करें।

A = 6,103, P = 5,000, n = 2
6,103 = 5,000 × (1 + R/100)^2
(1 + R/100)^2 = 6,103 / 5,000 = 1.2206
1 + R/100 = √1.2206 = 1.1057
R = 10.57%.

राशि = 6,103, मूलधन = 5,000, अवधि = 2 वर्ष
6,103 = 5,000 × (1 + दर/100)^2
(1 + दर/100)^2 = 6,103 / 5,000 = 1.2206
1 + दर/100 = √1.2206 = 1.1057
दर = 10.57%।

49. Find the amount on ₹9,500 after 3 years at 7% per annum compounded annually.
₹9,500 पर 7% वार्षिक दर से 3 वर्षों के बाद राशि ज्ञात करें।

A = 9,500 × (1 + 7/100)^3 = 9,500 × 1.225043 = ₹11,638.91.

राशि = 9,500 × (1 + 7/100)^3 = 9,500 × 1.225043 = ₹11,638.91।

50. The compound interest on ₹11,000 for 2 years is ₹2,420. Find the rate of interest.
₹11,000 पर 2 वर्षों के लिए चक्रवृद्धि ब्याज ₹2,420 है। ब्याज दर ज्ञात करें।

A = 11,000 + 2,420 = ₹13,420
13,420 = 11,000 × (1 + R/100)^2
(1 + R/100)^2 = 13,420 / 11,000 = 1.22
1 + R/100 = √1.22 = 1.1045
R = 10.45%.

राशि = 11,000 + 2,420 = ₹13,420
13,420 = 11,000 × (1 + दर/100)^2
(1 + दर/100)^2 = 13,420 / 11,000 = 1.22
1 + दर/100 = √1.22 = 1.1045
दर = 10.45%।

Simple & Compound Interest – 50 Questions with Answers (Hindi + English)

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