Simple Interest

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MATHEMATICS AND QUATITUATIVE Aptitude – SIMPLE INTEREST

Introduction

Money is not free and it costs to borrow the money. Normally, the borrower has to pay an extra amount in addition to the amount he had borrowed. i.e, to repay the loan, the borrower has to pay the sum borrowed and the interest.

Lender and Borrower

The person giving the money is called the lender and the person taking the money is the borrower.

Principal (sum)

Principal (or the sum) is the money borrowed or lent out for a certain period. It is denoted by P.

Interest

Interest is the extra money paid by the borrower to the owner (lender) as a form of compensation for the use of the money borrowed.

Simple Interest (SI)

If the interest on a sum borrowed for certain period is calculated uniformly, it is called simple interest(SI).

Amount (A)

The total of the sum borrowed and the interest is called the amount and is denoted by A

The statement “rate of interest 10% per annum” means that the interest for one year on a sum of Rs.100 is Rs.10. If not stated explicitly, rate of interest is assumed to be for one year.

Let Principal = P, Rate = R% per annum and Time = T years. Then
Simple Interest, SI = PRT/100

From the above formula , we can derive the followings
P=100×SI/RT
R=100×SI/PT
T=100×SI/PR

Some Formulae

If a sum of money becomes n times in T years at simple interest, then the rate of interest per annum can be given be R = 100(n−1)/T %
The annual instalment which will discharge a debt of D due in T years at R% simple interest per annum =100D/ (100T+RT(T-1)/2)
If an amount P₁ is lent out at simple interest of R₁% per annum and another amount P₂ at simple interest rate of R₂% per annum, then the rate of interest for the whole sum can be given by
R=(P1R1+P2R2)/ (P1+P2)
If a certain sum of money is lent out in n parts in such a manner that equal sum of money is obtained at simple interest on each part where interest rates are R₁, R₂, … , R_n respectively and time periods are T₁, T₂, … , T_n respectively, then the ratio in which the sum will be divided in n parts can be given by (1/R1T1):(1/R2T2):⋯(1/RnTn)
If a certain sum of money P lent out for a certain time T amounts to P₁ at R₁% per annum and to P₂at R₂% per annum, then P = (P2R1−P1R2)/ (R1−R2) and T = (P1−P2) ×100 years / (P2R1−P1R2)

SOLVED EXAMPLES

LEVEL 1

Arun took a loan of Rs. 1400 with simple interest for as many years as the rate of interest. If he paid Rs.686 as interest at the end of the loan period, what was the rate of interest?
A. 8%	B. 6%
C. 4%	D. 7%

Ans. Let rate = R%

Then, Time, T = R years

P = Rs.1400

SI = Rs.686

SI= PRT/100 ⇒ 686 = 1400 × R × R/100 ⇒ 686=14 R x R ⇒ 49=R x R ⇒ R=7

i.e.,Rate of Interest was 7%. (D)

How much time will it take for an amount of Rs. 900 to yield Rs. 81 as interest at 4.5% per annum of simple interest?
A. 2 years	B. 3 years
C. 1 year	D. 4 years

Ans. P = Rs.900

SI = Rs.81

T = ?

R = 4.5%

T= 100×SI/PR = 100×81/(900×4.5) = 2 years (A)

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. 700	B. Rs. 690
C. Rs. 650	D. Rs. 698

Ans. Simple Interest (SI) for 1 year = 854-815 = 39

Simple Interest (SI) for 3 years = 39 × 3 = 117

Principal = 815 – 117 = Rs.698 (D)

A sum fetched a total simple interest of Rs. 929.20 at the rate of 8 p.a. in 5 years. What is the sum?
A. Rs. 2323	B. Rs. 1223
C. Rs. 2563	D. Rs. 2353

Ans. SI = Rs.929.20

P = ?

T = 5 years

R = 8%

P = 100×SI/RT=100×929.20/(8×5) = Rs.2323 (A)

What will be the ratio of simple interest earned by certain amount at the same rate of interest for 5 years and that for 15 years?
A. 3 : 2	B. 1 : 3
C. 2 : 3	D. 3 : 1

Solution 1
Let Principal = P

Rate of Interest = R%

Required Ratio = (PR×5/100)/ (PR×15/100) = 1:3 (B)

Solution 2

Simple Interest = PRT100

Here Principal(P) and Rate of Interest (R) are constants

Hence, Simple Interest ∝ T

Required Ratio = Simple Interest for 5 years Simple Interest for 15 years=T1T2=515=13=1:3 (B)

A sum of money amounts to Rs.9800 after 5 years and Rs.12005 after 8 years at the same rate of simple interest. The rate of interest per annum is
A. 15%	B. 12%
C. 8%	D. 5%

Ans. Simple Interest for 3 years = (Rs.12005 – Rs.9800) = Rs.2205

Simple Interest for 5 years = 22053×5=Rs.3675

Principal (P) = (Rs.9800 – Rs.3675) = Rs.6125

R = 100×SI/PT=100×3675/(6125×5) =12% (B)

A lent Rs. 5000 to B for 2 years and Rs. 3000 to C 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. 10%
C. 7%	D. 8%

Ans. Let the rate of interest per annum be R%

Simple Interest for Rs. 5000 for 2 years at rate R% per annum +Simple Interest for Rs. 3000 for 4 years at rate R% per annum = Rs.2200

⇒5000×R×2/100+3000×R×4/100=2200

⇒100R + 120R=2200⇒220R=2200⇒R=10

i.e, Rate = 10%. (B)

In how many years, Rs. 150 will produce the same interest at 6% as Rs. 800 produce in 2 years at 4½% ?
A. 4 years	B. 6 years
C. 8 years	D. 9 years

Ans. Let Simple Interest for Rs.150 at 6% for n years = Simple Interest for Rs.800 at 4½ % for 2 years

150×6×n/100 = 800×4.5×2/100

150×6×n = 800×4.5×2

n = 8 years (C)

LEVEL 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. 7200
C. Rs. 6500	D. Rs. 7500

Ans. Let the Investment in scheme A be Rs.x

and the investment in scheme B be Rs. (13900 – x)

We know that SI = PRT/100

Simple Interest for Rs.x in 2 years at 14% p.a. = x×14×2100=28x100Simple Interest for Rs.(13900 – x) in 2 years at 11% p.a. = (13900−x)×11×2/100 =22(13900−x)/100

Total interest =Rs.3508

Thus, 28x/100+22(13900−x)/100 = 3508

28x+305800−22x=350800

6x = 45000

x=45000/6=7500

Investment in scheme B = 13900 – 7500 = Rs.6400 (A)

A certain sum in invested for T years. It amounts to Rs. 400 at 10% per annum. But when invested at 4% per annum, it amounts to Rs. 200. Find the time (T).
A. 45 years	B. 60 years
C. 40 years	D. 50 Years

Solution 1

Let the principal = Rs.x

and time = y years

Principal,x amounts to Rs.400 at 10% per annum in y years

Simple Interest = (400-x)

Simple Interest = PRT/100

⇒ (400−x) = x×10×y/100

⇒ (400−x) = xy/10— (equation 1)

Principal,x amounts to Rs.200 at 4% per annum in y years

Simple Interest = (200-x)

Simple Interest = PRT/100

⇒ (200−x) = x×4×y/100

⇒ (200−x) = xy/25— (equation 2)

(equation 1)/(equation2)

⇒ (400−x) / (200−x) = (xy/10)/(xy/25)

⇒ (400−x)/ (200−x) =25/10

⇒ (400−x)/ (200−x) =52

⇒ 800−2x = 1000−5x

⇒200=3x

⇒x =200/3 Substituting this value of x in Equation 1, we get,

(400−200/3) = (200y/3)/10

⇒ (400−200/3) = 20y/3

⇒ 1200−200=20y

⇒1000=20y

y=1000/20=50 years (D)

Solution 2

If a certain sum of money P lent out for a certain time T amounts to P₁ at R₁% per annum and to P₂ at R₂% per annum, then

P = (P2R1−P1R2)/ (R1−R2)

T = (P1−P2)x 100 years/(P2R1−P1R2)

R₁ = 10%, R₂ = 4%

P₁ = 400, P₂ = 200

T = (P1−P2)x 100 / (P2R1−P1R2) = (400−200)x 100 / (200×10−400×4)

=200 x 100/ (2000−1600) =200 ×100/400 = 12×100=50 years (D)

Mr. Mani invested an amount of Rs. 12000 at the simple interest rate of 10% per annum and another amount at the simple interest rate of 20% per annum. The total interest earned at the end of one year on the total amount invested became 14% per annum. Find the total amount invested.
A. Rs. 25000	B. Rs. 15000
C. Rs. 10000	D. Rs. 20000

Ans. If an amount P₁ is lent out at simple interest of R₁% per annum and another amount P₂ at simple interest rate of R₂% per annum, then the rate of interest for the whole sum can be given by

R= (P1R1+P2R2)/(P1+P2)

P₁ = Rs. 12000, R₁ = 10%

P₂ =? R₂ = 20%

R = 14%

14 = (12000×10+P2×20)/ (12000+P2)

12000×14+14P2 =120000+20P2

6P2=14×12000−120000=48000

⇒P2=8000

Total amount invested = (P₁ + P₂) = (12000 + 8000) = Rs. 20000 (D)

A sum of money is lent at S.I. for 6 years. If the same amount is paid at 4% higher, Arun would have got Rs. 120 more. Find the principal
A. Rs. 200	B. Rs. 600
C. Rs. 400	D. Rs. 500

Ans. This means, simple interest at 4% for that principal is Rs.120

P=100×SI/ RT=100×120/ (4×6) =100×30/6 = 100×5 = 500 (D)

The simple interest on Rs. 1820 from March 9, 2003 to May 21, 2003 at 7 ¹⁄₂% rate is
A. Rs. 27.30	B. Rs. 22.50
C. Rs. 28.80	D. Rs. 29

Ans. Time, T = (22 + 30 + 21) days = 73 days = 73/365 year=1/5 year

Rate, R = 7.5%=15/2%

SI = PRT/100 = 1820× (15/2) × (1/5)/100 = 1820 × (3/2)/100 = 910 × 3/100

= 2730/100 = 27.30 (A)

A sum of Rs. 7700 is to be divided among three brothers Vikas, Vijay and Viraj in such a way that simple interest on each part at 5% per annum after 1, 2 and 3 years respectively remains equal. The Share of Vikas is more than that of Viraj by
A. Rs.1200	B. Rs.1400
C. Rs.2200	D. Rs.2800

Ans. If a certain sum of money is lent out in n parts in such a manner that equal sum of money is obtained at simple interest on each part where interest rates are R₁, R₂, … , R_n respectively and time periods are T₁, T₂, … , T_n respectively, then the ratio in which the sum will be divided in n parts can be given by

1/R1T1:1/R2T2:⋯1/RnTn

T₁ = 1 , T₂ = 2, T₃ = 3

R₁ = 5 , R₂ = 5, R₃ = 5

Share of Vikas : Share of Vijay : Share of Viraj

= (1/5×1) : (1/5×2) : (1/5×3) = 1/1:1/2:1/3 = 6:3:2

Total amount is Rs. 7700

Share of Vikas = 7700×6/11=700×6 = 4200

Share of Viraj = 7700×2/11=700×2=1400

Share of Vikas is greater than Share of Viraj by (4200 – 1400) = Rs. 2800 (D)

David invested certain amount in three different schemes A, B and C with the rate of interest 10% p.a., 12% p.a. and 15% p.a. respectively. If the total interest accrued in one year was Rs. 3200 and the amount invested in Scheme C was 150% of the amount invested in Scheme A and 240% of the amount invested in Scheme B, what was the amount invested in Scheme B?
A. Rs.5000	B. Rs.2000
C. Rs.6000	D. Rs.3000

Ans. Let x, y and x be his investments in A, B and C respectively. Then

Then, Interest on x at 10% for 1 year

+ Interest on y at 12% for 1 year

+ Interest on z at 15% for 1 year

= 3200

x×10×1/100+y×12×1/100+z×15×1/100=3200

⇒10x+12y+15z=320000−−−(1)

Amount invested in Scheme C was 240% of the amount invested in Scheme B

=>z=240y/100 = 60y/25=12y/5−−−(2)

Amount invested in Scheme C was 150% of the amount invested in Scheme A

=>z=150x/100=3x/2

=>x=2z/3=2/3×12y/5=8y/5−−−(3)

From(1),(2) and (3),

10x + 12y + 15z = 320000

10(8y/5)+12y+15(12y/5)=320000

16y+12y+36y=320000

64y=320000

y=320000/64=10000/2=5000

i.e.,Amount invested in Scheme B = Rs.5000 (A)

Simple interest is a method of calculating interest on a loan or deposit. The formula for simple interest is:

$I = PRT$

Where:

$I$ is the simple interest earned
$P$ is the principal amount borrowed or deposited
$R$ is the interest rate as a Percentage
$T$ is the time in years

For example, if you borrow $100 at a 10% interest rate for 1 year, you will pay $10 in interest.

Simple interest is a straightforward way to calculate interest, but it can be inaccurate for long-term loans or deposits. This is because simple interest does not take into account the compounding of interest. Compounding is when interest is earned on both the principal amount and the interest that has already been earned. This can lead to a significant increase in the amount of interest earned over time.

To calculate Compound Interest, you can use the following formula:

$A = P(1 + r/n)^nt$

Where:

$A$ is the final amount
$P$ is the principal amount
$r$ is the interest rate as a percentage
$n$ is the number of times interest is compounded per year
$t$ is the number of years

For example, if you invest $100 at a 10% interest rate compounded annually for 1 year, you will have $110 at the end of the year. However, if you invest the same amount at the same interest rate compounded quarterly, you will have $110.25 at the end of the year. This is because the interest is earned on the interest that has already been earned, which leads to a higher final amount.

Compound interest can be a powerful tool for saving and investing. By taking advantage of compounding, you can grow your money much faster than you would with simple interest.

Simple interest is a common way to calculate interest on loans and deposits. It is a straightforward formula that can be used to calculate the amount of interest that will be earned. However, simple interest can be inaccurate for long-term loans or deposits. This is because simple interest does not take into account the compounding of interest. Compounding is when interest is earned on both the principal amount and the interest that has already been earned. This can lead to a significant increase in the amount of interest earned over time.

Compound interest can be a powerful tool for saving and investing. By taking advantage of compounding, you can grow your money much faster than you would with simple interest.

What is compound interest?

Compound interest is interest that is calculated on the principal amount and on any interest that has already been earned. This means that the interest you earn in one period is added to the principal amount, and then interest is calculated on the new, larger amount. This can lead to exponential Growth in the amount of money you have over time.

How does compound interest work?

Let’s say you invest \$100 at a 5% annual interest rate compounded annually. After one year, you will have earned \$5 in interest. This \$5 is added to your principal amount, so you now have \$105. The next year, you will earn interest on the entire \$105, which is \$5.25. This process continues year after year, and your investment will grow at an ever-increasing rate.

What are the benefits of compound interest?

The main benefit of compound interest is that it can help you grow your money much faster than simple interest. With simple interest, you only earn interest on the principal amount. With compound interest, you earn interest on the principal amount and on any interest that has already been earned. This can lead to exponential growth in the amount of money you have over time.

What are the risks of compound interest?

The main risk of compound interest is that it can also lead to your debt growing much faster than you might expect. If you have a loan with a high interest rate, the interest you owe will be compounded each month, and your debt will grow quickly. This is why it’s important to pay off your debt as quickly as possible.

How can I use compound interest to my advantage?

There are a few things you can do to use compound interest to your advantage:

Start saving early. The earlier you start saving, the more time your money has to grow.
Invest your money. Investing your money can help you earn a higher return than you would on a Savings account.
Choose a high-interest savings account. There are a number of savings accounts available that offer high interest rates.
Pay off your debt. If you have debt, make sure to pay it off as quickly as possible. The longer you wait, the more interest you will accrue.

What is the difference between simple interest and compound interest?

Simple interest is interest that is calculated only on the principal amount. Compound interest is interest that is calculated on the principal amount and on any interest that has already been earned. This means that the interest you earn in one period is added to the principal amount, and then interest is calculated on the new, larger amount. This can lead to exponential growth in the amount of money you have over time.

What is the formula for compound interest?

The formula for compound interest is:

$A = P(1 + r/n)^nt$

where:

$A$ is the future value of the investment
$P$ is the principal amount
$r$ is the annual interest rate
$n$ is the number of times interest is compounded per year
$t$ is the number of years the investment is held

What is the rule of 72?

The rule of 72 is a shortcut for estimating how long it will take for an investment to double at a given interest rate. To use the rule of 72, divide 72 by the interest rate. The result is the number of years it will take for your investment to double. For example, if you invest \$100 at a 6% interest rate, it will take about 12 years to double your money.

What is the magic number 72?

The magic number 72 is a shortcut for estimating how long it will take for an investment to double at a given interest rate. To use the rule of 72, divide 72 by the interest rate. The result is the number of years it will take for your investment to double. For example, if you invest \$100 at a 6% interest rate, it will take about 12 years to double your money.

What is the 80/20 rule?

The 80/20 rule is a principle that states that 80% of the effects come from 20% of the causes. This rule can be applied to many different areas of life, including investing. In investing, the 80/20 rule suggests that 80% of your investment returns will come from 20% of your investments. This means that it is important to focus your investment efforts on the investments that have the greatest potential for return.

**What is the 10

Sure, here are some MCQs without mentioning the topic Simple Interest:

What is the formula for calculating simple interest?
What is the difference between simple interest and compound interest?
What is the annual percentage rate (APR)?
What is the effective annual rate (EAR)?
What is the Rule of 72?
What is the present value of a future sum of money?
What is the future value of a present sum of money?
What is the annuity due?
What is the ordinary annuity?
What is the amortization schedule?

Here are the answers to the MCQs:

The formula for calculating simple interest is $I = PRT$, where $I$ is the interest, $P$ is the principal, $R$ is the interest rate, and $T$ is the time period.
The difference between simple interest and compound interest is that simple interest is calculated only on the principal amount, while compound interest is calculated on the principal amount plus any interest that has already been earned.
The annual percentage rate (APR) is the interest rate that is charged on a loan or investment, expressed as a yearly percentage.
The effective annual rate (EAR) is the actual rate of return on an investment, taking into account compounding.
The Rule of 72 is a shortcut for estimating the number of years it will take to double your money at a given interest rate. To use the Rule of 72, divide 72 by the interest rate.
The present value of a future sum of money is the amount of money that you would need to invest today in order to have the desired future sum of money.
The future value of a present sum of money is the amount of money that you will have in the future if you invest a certain amount of money today at a given interest rate.
An annuity due is an annuity in which the payments are made at the beginning of each period.
An ordinary annuity is an annuity in which the payments are made at the end of each period.
An amortization schedule is a table that shows the amount of each payment on a loan, as well as the interest and principal that is paid with each payment.