At what rate of compound interest per annum will a sum of rupees 12000 Become 1348.32 in 2 years?

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

MODERATE

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:

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.

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

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

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

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.

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

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.

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

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

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

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.

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

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

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

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.

At what rate of compound interest per annum will a sum of rupees 12000 rupees 1348.32 in 2 years?

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