The rate of interest on a sum of money is 4.5% per annum

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Solution

The correct option is D 4%
Let the principal be Rs x. then the simple interest (I)=425x.
Let the rate of interest p.a. be r%, then time (T)=r years.
∴R=100×IP×T⇒r=100×425xx×r⇒r2=40025orr=205=4%

Solve

Textbooks

Question Papers

Aptitude

Topic: Simple Interest and Compound Interest

 Study Material

Concept 1: Understanding important terms.

• Interest: Interest is payment from a borrower or deposit-taking financial institution to a lender or depositor of an amount above repayment of the principal sum, at a particular rate.

• Rate of Interest:  An interest rate is the percentage of principal charged by the lender for the use of its money.

• Principal: Principal refers to the original sum of money borrowed in a loan or put into an investment. 

• Final Amount: Final amount refers to total amount (Principal amount and Interest) to be paid back to the lender. 

• Let’s identify these terms in a problem. An amount of Rs.20000 was lend to a borrower for two years at an interest rate of 3% SI. The borrower paid back Rs.21200 to the lender after two years. Here, amount Rs.20000 refers to the principal amount, Two years refers to time by which loan amount along with interest is to be paid back, 3% refers to the percentage of principal charged by the lender and Rs.21200 refers to final amount liable to be paid back to the lender.

Concept 2: Understanding Simple interest & Compound interest.

• Simple Interest: Simple interest is the method of calculating the interest amount for some principal amount of money. Simple interest is calculated on the principal, or original, amount of a loan.

• Compound Interest: Compound interest is the method of calculating the interest amount for some principal amount of money. Compound interest (or compounding interest) is the interest on a loan or deposit calculated based on both the initial principal and the accumulated interest from previous periods. It is different from the simple interest where interest is not added to the principal while calculating the interest during the next period. Compound interest finds its usage in most of the transactions in the banking and finance sectors and also in other areas as well. Some of its applications are:

• Increase or decrease in population.

• The growth of bacteria.

• Rise or depreciation in the value of a product.

Compound interest formula is given by: Compound interest = (Amount – Principal) Where the amount is given by,

Where,

A= Amount, P= Principal, R= Rate of interest and T= Time (in years)

Derivation of compound interest formula:

Concept 3: Compound Interest VS Simple Interest:

• As we know that, the major difference between simple interest and compound interest is that in simple interest, interest is calculated on the principal or original sum every year whereas in compound interest, interest is calculated on the principal and also on the interest earned over the years also called interest on interest. Let’s understand the difference between two interests through below example:

Concept 4: Understanding calculation of SI & CI though percentages:

• In your previous sessions you have studied concept of percentages, about multiplying factor etc. now its time to utilise those concepts in solving SI and CI problems. Let us see some examples.

Example 1: What is SI of Rs.800 on 5% per annum for 3 years?

We can either put formula and calculate as below:

SI= (800*5*3)/100 = 120

Or,

As we know that in simple interest, interest is always calculated on principal so we can just calculate 15% (5% for 3 years) of 800 which is 120. Thus, in this way we don’t have to remember the formula and we can simply get answers by using concept of percentages.

Example 2: What will be the CI obtained on an amount of Rs.4800 at the rate of 5% for 3 years?

We can either put formula and calculate as below:

Amount= 4800[1+ (5/100)]^3 = 5556.6 ; CI= (5556.6 – 4800)= 756.6

Or,

We can simply use concept of multiplying factor learnt in percentages, since 4800 is increasing by 5% every year for constant 3 years, we can write it as  4800* (1.05)^3 = 5556.6 ; CI = (5556.6-4800) = 756.6.

Thus, in this way we don’t have to remember the complex formula of CI and we easily solve problems based on CI through concept of multiplying factor learnt in session of percentage.

Problems on Simple Interest and Compound Interest

Foundation

1.	A sum of money at simple interest amounts to Rs. 815 in 3 years and to Rs. 854 in 4 years. The sum is:
A. Rs. 650 B. Rs. 690 C. Rs. 698 D. Rs. 700
2.	Mr. Thomas invested an amount of Rs. 13,900 divided in two different schemes A and B at the simple interest rate of 14% p.a. and 11% p.a. respectively. If the total amount of simple interest earned in 2 years be Rs. 3508, what was the amount invested in Scheme B?
A. Rs. 6400 B. Rs. 6500 C. Rs. 7200 D. Rs. 7500 E. None of these
3.	A sum fetched a total simple interest of Rs. 4016.25 at the rate of 9 p.c.p.a. in 5 years. What is the sum?
A. Rs. 4462.50 B. Rs. 8032.50 C. Rs. 8900 D. Rs. 8925 E. None of these
4.	How much time will it take for an amount of Rs. 450 to yield Rs. 81 as interest at 4.5% per annum of simple interest?
A. 3.5 years B. 4 years C. 4.5 years D. 5 years

5.	Reena took a loan of Rs. 1200 with simple interest for as many years as the rate of interest. If she paid Rs. 432 as interest at the end of the loan period, what was the rate of interest?
A. 3.6 B. 6 C. 18 D. Cannot be determined E. None of these

MODERATE

1.	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?
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. None of these
3.	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

4.	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:

5.	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

HOTS-HIGH ORDER THINKING SKILLS

1.	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
2.	The compound interest on Rs. 30,000 at 7% per annum is Rs. 4347. The period (in years) is:

3.	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
4.	At what rate of compound interest per annum will a sum of Rs. 1200 become Rs. 1348.32 in 2 years?
5.	The least number of complete years in which a sum of money put out at 20% compound interest will be more than doubled is:

SOLUTIONS

FOUNDATION

1. Answer: Option C

Explanation:

S.I. for 1 year = Rs. (854 – 815) = Rs. 39.

S.I. for 3 years = Rs.(39 x 3) = Rs. 117.

 Principal = Rs. (815 – 117) = Rs. 698.

2. Answer: Option A

Explanation:

Let the sum invested in Scheme A be Rs. x and that in Scheme B be Rs. (13900 – x).

Then,		x x 14 x 2		+		(13900 – x) x 11 x 2		= 3508
100	100

 28x – 22x = 350800 – (13900 x 22)

 6x = 45000

 x = 7500.

So, sum invested in Scheme B = Rs. (13900 – 7500) = Rs. 6400.

3. Answer: Option D

Explanation:

Principal	= Rs. 100 x 4016.25 9 x 5
	= Rs. 401625 45
	= Rs. 8925.

4. Answer: Option B

Explanation:

Time =		100 x 81	years	= 4 years.
450 x 4.5

5. Answer: Option B

Explanation:

Let rate = R% and time = R years.

Then,		1200 x R x R		= 432
100

 12R2 = 432

 R2 = 36

 R = 6.

MODERATE

1. Answer: Option D

Explanation:

S.I. = Rs. (15500 – 12500) = Rs. 3000.

Rate =		100 x 3000	%	= 6%
12500 x 4

2. Answer: Option B

Explanation:

Let the sum be Rs. 100. Then,

S.I. for first 6 months = Rs.		100 x 10 x 1		= Rs. 5
100 x 2

S.I. for last 6 months = Rs.		105 x 10 x 1		= Rs. 5.25
100 x 2

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

 Effective rate = (110.25 – 100) = 10.25%

3. Answer: Option B

Explanation:

Amount	= Rs. 1600 x 1 + 5 2 + 1600 x 1 + 5 2 x 100 2 x 100
	= Rs. 1600 x 41 x 41 + 1600 x 41 40 40 40
	= Rs. 1600 x 41 41 + 1 40 40
	= Rs. 1600 x 41 x 81 40 x 40
	= Rs. 3321.

 C.I. = Rs. (3321 – 3200) = Rs. 121

4. Answer: Option A

Explanation:

Let the sum be Rs. x. Then,

C.I. =		x		1 +	4		2	– x		=		676	x	– x		=	51	x.
100	625	625

S.I. =		x x 4 x 2		=	2x	.
100	25

	51x	–	2x	= 1
625	25

 x = 625.

5. Answer: Option C

Explanation:

Let P = Rs. 100. Then, S.I. Rs. 60 and T = 6 years.

R =		100 x 60		= 10% p.a.
100 x 6

Now, P = Rs. 12000. T = 3 years and R = 10% p.a.

C.I.	= Rs. 12000 x 1 + 10 3 – 1 100
	= Rs. 12000 x 331 1000
	= 3972.

SOLUTIONS

FOUNDATION

1. Answer: Option C

Explanation:

S.I. for 1 year = Rs. (854 – 815) = Rs. 39.

S.I. for 3 years = Rs.(39 x 3) = Rs. 117.

 Principal = Rs. (815 – 117) = Rs. 698.

2. Answer: Option A

Explanation:

Let the sum invested in Scheme A be Rs. x and that in Scheme B be Rs. (13900 – x).

Then,		x x 14 x 2		+		(13900 – x) x 11 x 2		= 3508
100	100

 28x – 22x = 350800 – (13900 x 22)

 6x = 45000

 x = 7500.

So, sum invested in Scheme B = Rs. (13900 – 7500) = Rs. 6400.

3. Answer: Option D

Explanation:

Principal	= Rs. 100 x 4016.25 9 x 5
	= Rs. 401625 45
	= Rs. 8925.

4. Answer: Option B

Explanation:

Time =		100 x 81	years	= 4 years.
450 x 4.5

5. Answer: Option B

Explanation:

Let rate = R% and time = R years.

Then,		1200 x R x R		= 432
100

 12R2 = 432

 R2 = 36

 R = 6.

MODERATE

1. Answer: Option D

Explanation:

S.I. = Rs. (15500 – 12500) = Rs. 3000.

Rate =		100 x 3000	%	= 6%
12500 x 4

2. Answer: Option B

Explanation:

Let the sum be Rs. 100. Then,

S.I. for first 6 months = Rs.		100 x 10 x 1		= Rs. 5
100 x 2

S.I. for last 6 months = Rs.		105 x 10 x 1		= Rs. 5.25
100 x 2

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

 Effective rate = (110.25 – 100) = 10.25%

3. Answer: Option B

Explanation:

Amount	= Rs. 1600 x 1 + 5 2 + 1600 x 1 + 5 2 x 100 2 x 100
	= Rs. 1600 x 41 x 41 + 1600 x 41 40 40 40
	= Rs. 1600 x 41 41 + 1 40 40
	= Rs. 1600 x 41 x 81 40 x 40
	= Rs. 3321.

 C.I. = Rs. (3321 – 3200) = Rs. 121

4. Answer: Option A

Explanation:

Let the sum be Rs. x. Then,

C.I. =		x		1 +	4		2	– x		=		676	x	– x		=	51	x.
100	625	625

S.I. =		x x 4 x 2		=	2x	.
100	25

	51x	–	2x	= 1
625	25

 x = 625.

5. Answer: Option C

Explanation:

Let P = Rs. 100. Then, S.I. Rs. 60 and T = 6 years.

R =		100 x 60		= 10% p.a.
100 x 6

Now, P = Rs. 12000. T = 3 years and R = 10% p.a.

C.I.	= Rs. 12000 x 1 + 10 3 – 1 100
	= Rs. 12000 x 331 1000
	= 3972.

HOTS-HIGH ORDER THINKING SKILLS

1. Answer: Option A

Explanation:

C.I. when interest compounded yearly	= Rs. 5000 x 1 + 4 x 1 +  x 4 100 100
	= Rs. 5000 x 26 x 51 25 50
	= Rs. 5304.

C.I. when interest is compounded half-yearly
	= Rs. 5000 x 51 x 51 x 51 50 50 50
	= Rs. 5306.04

• Difference = Rs. (5306.04 – 5304) = Rs. 2.04

2. Answer: Option A

Explanation:

Amount = Rs. (30000 + 4347) = Rs. 34347.

Let the time be n years.

Then, 30000		1 +	7		n	= 34347
100

		107		n	=	34347	=	11449	=		107		2
100	30000	10000	100

 n = 2 years.

3. Answer: Option C

Explanation:

Amount	= Rs. 25000 x 1 + 12 3 100
	= Rs. 25000 x 28 x 28 x 28 25 25 25
	= Rs. 35123.20

• C.I. = Rs. (35123.20 – 25000) = Rs. 10123.20

4. Answer: Option A

Explanation:

Let the rate be R% p.a.

Then, 1200 x		1 +	R		2	= 1348.32
100

		1 +	R		2	=	134832	=	11236
100	120000	10000

1 +	R	=	106
100	100

 R = 6%

5. Answer: Option B

Explanation:

P		1 +	20		n	> 2P			6		n	> 2.
100	5

Now,		6	x	6	x	6	x	6		> 2.
5	5	5	5

So, n = 4 years.