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# Simple Interest and Compound Interest Problems and Solutions

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NEW In the competitive exams, two types of interest questions asked, first is simple interest and second is compound interest. Both types are important by the perspective of SSC and Banking exams.

So, here are given simple interest and compound interest problems and solutions for your preparation. If you want to save your time in competitive exams, you should practice these problems with solutions.

As well as you can understand easily about Simple and Compound Interest Formulas that how to use formulas in these types of questions.

## Problems with Solutions of Simple and Compound Interest

Q.1. The difference between Compound Interest and Simple Interest on a certain sum of money at 10 % per annum for 3 years is Rs. 930. Find the principal if it is known that the interest is compounded annually.

(A) 30000

(B) 35000

(C) 40000

(D) 45000

(E) None of these

Ans .   A

The Simple Interest after three years @ 10% is 30%.

The Compound Interest after 3 years @ 10% will be 1.1 × 1.1 × 1.1 = 1.331

Cumulative rate of Interest is 33.1%.

Here, the difference after 3 years is 3.1% and in the question, it is given to be Rs. 930.

Thus, the Principal is 930 × (100/3.1) = Rs. 30000.

Q.2. An automobile financier claims to be lending money at simple interest, but he includes the interest every six months for calculating the principal. If he is charging an interest of 10%, the effective rate of interest becomes:

(A) 10%

(B) 10.25%

(C) 10.5%

(D) Data inadequate

(E) None of these

Ans .   B

Let the sum be Rs.100. Then,

S.I. for first 6 months

= Rs. [100 × 10 × 1  / 100 × 2] = Rs.5

S.I. for last 6 months = Rs. [105 × 10 × 1  / 100 × 2] = Rs.5.25

So, amount at the end of 1 year = Rs. (100 + 5 + 5.25) = Rs.110.25

So, effective rate = (110.25 ⎯ 100) = 10.25%

Q.3. The simple interest on a sum of money in 5 years at 12 % per annum is Rs. 400 less than the simple interest accrued on the same sum in 7 years at 10 % per annum. Find the sum.

(A) 3500

(B) 4000

(C) 4500

(D) 2500

(E) None of these

Ans .   B

Let the sum be P.

→ SI in 5 years at 12 % per annum = P x 12 x 5 / 100 = 0.6 P

→ SI in 7 years at 10 % per annum = P x 10 x 7 / 100 = 0.7 P

Now, according to the question,

0.7 P – 0.6 P = 400

→ 0.1 P = 400

→ P = 4000

Thus, the required sum is Rs. 4000

Q.4. Aman took a loan from a bank at the rate of 12% p.a. simple interest. After 3 years he had to pay Rs. 5400 interest only for the period. The principal amount borrowed by him was:

(A) Rs. 2000

(B) Rs. 10,000

(C) Rs. 15,000

(D) Rs. 20,000

(E) None of these

Principal = Rs. [ 100 × 5400  / 12 × 3] = Rs.15000

Q.5. If Rs. 5000 amounts to Rs. 5832 in two years compounded annually, find the rate of interest per annum.

(A) 6.8%

(B) 7.1%

(C) 8%

(D) 9%

(E) None of these

Ans .   C

Here, P = 5000, A = 5832, n = 2

A = P [1 + (R / 100)]n

→ 5832 = 5000 [1 + (R / 100)]2

→ [1 + (R / 100)]2 = 5832 / 5000

→ [1 + (R / 100)]2 = 11664 / 10000

→ [1 + (R / 100)] = 108 / 100

→ R / 100 = 8 / 100

→ R = 8 %

Thus, the required rate of interest per annum in 8 %

Q.6. A sum of Rs. 12,500 amounts to Rs. 15,500 in 4 years at the rate of simple interest. What is the rate of interest?

(A) 3%

(B) 4%

(C) 5%

(D) 6%

(E) None of these

Ans .   D

S.I. = Rs. (15500 ⎯ 12500) = Rs.3000

Rate = [ (100 × 3000) / (12500 × 4) ]% = 6%

Q.7.  A sum of Rs. 1000 is to be divided among two brothers such that if the interest being compounded annually is 5 % per annum, then the money with the first brother after 4 years is equal to the money with the second brother after 6 years.

(A) 425 and 498

(B) 400 and 489

(C) 500 and 575

(D) 524.38 and  475.62

(E) None of these

Ans .   D

Let the first brother be given Rs. P

→ Money with second brother = Rs. 1000 – P

Now, according to the question,

P [1 + (5 / 100)]4 = (1000 – P) [1 + (5 / 100)]6

→P (1.05)4 = (1000 – P) (1.05)6

→ 0.9070 P = 1000 – P

→ 1.9070 P = 1000

→ P = 524.38

Therefore, share of first brother = Rs. 524.38

Share of second brother = Rs. 475.62

Q.8. Aastha lent Rs. 5000 to Bahubali for 2 years and Rs. 3000 to Chinky for 4 years on simple interest at the same rate of interest and received Rs. 2200 in all from both of them as interest. The rate of interest per annum is:

(A) 5%

(B) 7%

(C) 7 1/8%

(D) 10%

(E) None of these

Ans .   D

Let the rate be R% p.a.

Then, [ 500 × R × 2  / 100 ] + [300 × R × 4  / 100] = 2200

100R + 120R = 2200

R = [2200  / 220] = 10

So, rate = 10%

Q.9. A sum of Rs. 1000 was lent to two people, one at the rate of 5 % and other at the rate of 8 %. If the simple interest after one year is Rs. 62, find the sum lent at each rate.

(A) 400, 600

(B) 800, 1200

(C) 300, 500

(D) 700, 900

(E) None of these

Ans .   A

Let the sum lent at 5 % be P.

→ Sum lent at 8 % = 1000 – P

Now, according to the question,

SI for 5 % + SI for 8 % = 62

→ (P x 5 x 1 / 100) + ((1000 – P) x 8 x 1 / 100) =62

→ 5 P + 8 (1000 – P) = 6200

→ 5 P + 8000 – 8 P = 6200

→ 3 P = 1800

→ P = 600

Therefore, sum lent at 5 % = P = Rs. 600

Sum lent at 8 % = 1000 – P = Rs. 400

Q.10. Find the compound interest on Rs. 3000 at 5% for 2 years, compounded annually.

(A) 307.5

(B) 3307.5

(C) 3000.5

(D) 3100

Ans .  A

Amount with CI = 3000 (1+ 5/100)2 = Rs. 3307.5

Therefore, CI = 3307.5 – 3000 = Rs. 307.5

If you are facing any problem in the simple and compound interest problems and solutions, ask me in the comment section without any hesitation.

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### Vikram Singh

Providing knowledgable questions of Reasoning and Aptitude for the competitive exams.

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