On what principal will the simple interest be $Rs.\,7,008$ in $6$ years $3$ months at $5\%$ per year?
Answer
Verified
Hint: Here we have been given a simple interest value for which we have to calculate the principal amount for a given time at a given rate. Firstly as the time has to be in years we will convert the months in years as well. Then we will write down the formula for finding simple interest on an amount. Finally we will substitute all the values in the formula and simplify it to get the desired answer.
Complete step by step answer:
We have been given the following
information:
Simple Interest $I=Rs.\,7,008$ …..$\left( 1 \right)$
Time $T=6$ Years $3$ months …..$\left( 2 \right)$
As we know $12$ Months $=1$ year
$\Rightarrow 1$ Month $=\dfrac{1}{12}$ year
So as we have to convert $3$ months in year we will multiply by $3$ on both side and get,
$\Rightarrow 3$ Month $=\dfrac{3}{12}$ year
$\Rightarrow 3$ Month $=\dfrac{1}{4}$ years
On substituting the above value in equation (2) we get,
$T=6\times \dfrac{1}{4}$ Years
$\Rightarrow
T=\dfrac{25}{4}$ Years …..$\left( 3 \right)$
Rate $R=5\%$ …..$\left( 4 \right)$
Next as we have been given the value of simple interest and we have to find the principal amount we will use the Simple Interest formula.Now the formula for finding the simple Interest is as follows:
Simple Interest $I=\dfrac{P\times R\times T}{100}$
On substituting values from equation (1), (3) and (4) in above formula we get,
$7008=\dfrac{P\times \dfrac{25}{4}\times 5}{100}$
$\Rightarrow
7008\times 100=P\times \dfrac{125}{4}$
Keep $P$ on one side and take the rest value on another as follows:
$P=\dfrac{7008\times 100\times 4}{125}$
$\therefore P=Rs.\,22,425.60$
On $Rs.\,22,425.60$ the simple interest be $Rs.\,7,008$ in $6$ years $3$ months at $5\%$ per year.
Note: Simple Interest is a method to calculate the interest amount on a principal amount of money for a given time period with the rate specified. It is only applied to the principal amount for the time period given. It is different from the profit as the interest is received by the lender and not the borrower whereas in profit the interest is received by the borrower. It is generally used when we borrow money from a bank.
Question
On what principal will the simple interest be Rs 7,008 in 6 years 3 months at 5% per year?
Hint:
Use the formula for simple interest and then find the principal amount.
The correct answer is: 22425.6 Rupees
Complete step by step solution:
Let the sum of money = P
We calculate simple interest by the formula,…(i)
where P is Principal amount, T is number of years and R is rate of interest
Here, we have T = 6 years and 3 months = 6.25 years, R = 5% , SI = 7008 and P = ?
On substituting the known values in (i), we
get Hence the sum of money P = 22425.6 Rupees.
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Related Questions to study
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Arun borrowed Rs 24,000 from Rahul at the rate of 15% per annum simple interest for 4 years. Find the simple interest and the total amount that has to be paid at the end of 4 years.
Complete step by step solution:
We calculate simple interest by the
formula,…(i)
where P is Principal amount, T is number of years and R is rate of interest
Money borrowed by Arun from Rahul = P = 24000 Rs
Here, we have T = 4,R = 15% and P = 24000
On substituting the known values in (i), we get
We have SI = 14400 Rupees.
We know the formula for total amount = A = P + SI…(ii)
where A is the total amount, P is the principal amount and SI is simple interest.
On substituting the known values in (ii), we get A = 24000 + 14400 =
38400
Hence total amount to be paid after 4 years = A = 38400 Rupees.
Arun borrowed Rs 24,000 from Rahul at the rate of 15% per annum simple interest for 4 years. Find the simple interest and the total amount that has to be paid at the end of 4 years.
Maths-General
Complete step by step solution:
We calculate simple interest by the formula,…(i)
where P is Principal amount, T is number of
years and R is rate of interest
Money borrowed by Arun from Rahul = P = 24000 Rs
Here, we have T = 4,R = 15% and P = 24000
On substituting the known values in (i), we get
We have SI = 14400 Rupees.
We know the formula for total amount = A = P + SI…(ii)
where A is the total amount, P is the principal amount and SI is simple interest.
On substituting the known values in (ii), we get A = 24000 + 14400 = 38400
Hence total amount to be paid after 4 years = A = 38400
Rupees.
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The simple interest on a certain sum of money is Rs 1480 for 2 years at 10% per year. Find the sum of money.
Complete step by step solution:
Let the sum of money = P
We calculate simple interest by the formula,…(i)
where P is Principal amount, T is number of years and R is rate of interest
Here, we
have T = 2,R = 10%, SI = 1480 and P = ?
On substituting the known values in (i), we get
Hence the sum of money P = 7400 Rupees.
The simple interest on a certain sum of money is Rs 1480 for 2 years at 10% per year. Find the sum of money.
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Complete step by step solution:
Let the sum of money = P
We calculate simple interest by the formula,…(i)
where P is Principal amount, T is
number of years and R is rate of interest
Here, we have T = 2,R = 10%, SI = 1480 and P = ?
On substituting the known values in (i), we get
Hence the sum of money P = 7400 Rupees.
Maths-
Find the simple interest and amount on Rs 5000 in 3 years at 8% p.a.
Complete step by step solution:
We calculate simple interest by
the formula,…(i)
where P is Principal amount, T is number of years and R is rate of interest
Here, we have T = 3,R = 8% and P = 5000
On substituting the known values in (i), we get
We have SI = 1200 Rupees.
We know the formula for total amount = A = P + SI…(ii)
where A is the total amount, P is the principal amount and SI is simple interest.
On substituting the known values in (ii), we get A = 5000 + 1200 = 6200
Hence total amount to be paid after 3 years = A = 6200
Rupees.
Find the simple interest and amount on Rs 5000 in 3 years at 8% p.a.
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Complete step by step solution:
We calculate simple interest by the formula,…(i)
where P is Principal amount, T is number of years and R is rate of interest
Here, we have T = 3,R = 8% and P = 5000
On substituting the known values in (i), we get
We have SI = 1200 Rupees.
We know the formula for total
amount = A = P + SI…(ii)
where A is the total amount, P is the principal amount and SI is simple interest.
On substituting the known values in (ii), we get A = 5000 + 1200 = 6200
Hence total amount to be paid after 3 years = A = 6200 Rupees.
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Find the amount to be paid at the end of 3 years, if principal is Rs 1800 at 9% p.a.
Complete step by step solution:
We calculate simple interest by the formula,…(i)
where P is Principal amount, T is number of years and R is rate of interest
Here, we have T = 3,R = 9% and P = 1800
On substituting the known values in (i), we get
We have SI = 486 Rupees.
We know the formula for total amount = A = P +SI…(ii)
where A is the total amount, P is the principal amount and SI is simple interest.
On substituting the
known values in (ii), we get A = 1800 + 486 = 2286
Hence total amount to be paid after 3 years = A = 2286 Rupees.
Find the amount to be paid at the end of 3 years, if principal is Rs 1800 at 9% p.a.
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Complete step by step solution:
We calculate simple interest by the formula,…(i)
where P is Principal amount, T is number of years and R is rate of interest
Here, we have
T = 3,R = 9% and P = 1800
On substituting the known values in (i), we get
We have SI = 486 Rupees.
We know the formula for total amount = A = P +SI…(ii)
where A is the total amount, P is the principal amount and SI is simple interest.
On substituting the known values in (ii), we get A = 1800 + 486 = 2286
Hence total amount to be paid after 3 years = A = 2286 Rupees.
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Find the compound interest for 3 years on Rs 5000, if the rate of interest for the successive years are 8%, 6% and 10% respectively.
Complete step by step solution:
Given that principal amount P = 5000
Number of years T = 3
Let R1 = 8%,R2 = 6% and R3 = 10%
Total amount , …(i)
On substituting the known values in (i), we get
We know that, Compound interest ( CI)
= total amount (A) - principal amount (P)
So, Compound interest ( CI) = 6296.4 - 5000 = 1296.4 Rupees
Find the compound interest for 3 years on Rs 5000, if the rate of interest for the successive years are 8%, 6% and 10% respectively.
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Complete step by step solution:
Given that principal amount P = 5000
Number of years T = 3
Let R1 = 8%,R2 = 6% and
R3 = 10%
Total amount , …(i)
On substituting the known values in (i), we get
We know that, Compound interest ( CI) = total amount (A) - principal amount (P)
So, Compound interest ( CI) = 6296.4 - 5000 = 1296.4 Rupees
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What annual instalment will discharge a debt of Rs 1092 due in 3 years at 12% simple interest?
Complete step by step solution:
Let the principal amount P = 1092
It is given that T = 2, R = 12%
We have the formula for annual payment …(i)
On substituting the known values in (i), we get
So, 325 Rupees is the annual instalment.
What annual instalment will discharge a debt of Rs 1092 due in 3 years at 12% simple interest?
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Complete step by step
solution:
Let the principal amount P = 1092
It is given that T = 2, R = 12%
We have the formula for annual payment …(i)
On substituting the known values in (i), we get
So, 325 Rupees is the annual instalment.
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What sum of money lent out at 6% for 2 years will produce the same interest as Rs. 1200 lent out at 5% for 3 years.
Complete step by step solution:
We calculate simple interest by the formula, …(i)
where P is Principal amount, T is number of years and R is rate of interest
Case Ⅰ
Let the sum of money = P
Here, we have
On substituting the values in (i), we get …(ii)
Case Ⅱ
Here, we have
On substituting the values in (i), we get …(iii)
It is given that the interest produced in both the cases is the same.
So,
Equate (ii) and (iii)
On equating, we get
rupees.
Hence the sum of money P = 1500 Rupees
What sum of money lent out at 6% for 2 years will produce the same interest as Rs. 1200 lent out at 5% for 3 years.
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Complete step by step solution:
We calculate simple interest by the formula, …(i)
where P is Principal amount, T is number of years and R is rate of
interest
Case Ⅰ
Let the sum of money = P
Here, we have
On substituting the values in (i), we get …(ii)
Case Ⅱ
Here, we have
On substituting the values in (i), we get …(iii)
It is given that the interest produced in both the cases is the same.
So, Equate (ii) and (iii)
On equating, we get
rupees.
Hence the sum of money P = 1500 Rupees
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What sum of money lent out at 5% for 3 years will produce the same interest as Rs. 900 lent out at 4% for 5 years.
Complete step by step solution:
We calculate simple interest by the formula, …(i)
where P is Principal amount, T is number of years and R is rate of interest
Case Ⅰ
Let the sum of money = P
Here, we have
On
substituting the values in (i), we get …(ii)
Case Ⅱ
Here, we have
On substituting the values in (i), we get …(iii)
It is given that the interest produced in both the cases is the same.
So, Equate (ii) and (iii)
On equating, we get
rupees.
Hence the sum of money P = 1200 Rupees
What sum of money lent out at 5% for 3 years will produce the same interest as Rs. 900 lent out at 4% for 5 years.
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Complete step by step solution:
We calculate simple interest by the formula, …(i)
where P is Principal amount, T is number of years and R is rate of interest
Case Ⅰ
Let the sum of money = P
Here, we have
On substituting the values in (i), we get …(ii)
Case Ⅱ
Here, we have
On substituting the values in (i), we get …(iii)
It is given that the interest produced in both the cases is the same.
So, Equate
(ii) and (iii)
On equating, we get
rupees.
Hence the sum of money P = 1200 Rupees
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Find the sum which will amount to Rs. 364.80 at 3 % per annum in 8 years at simple interest
Complete step by step solution:
Let the sum of money = P
We know the formula for total amount = A = P + SI
where A is the
total amount, T is the principal amount and R is simple interest.
We know that
where P is Principal amount, T is number of years and R is rate of interest
So, …(i)
Here, we have
On substituting these values in (i), we get
On further simplifications, we get
Hence the sum of money P = Rs 285.
Find the sum which will amount to Rs. 364.80 at 3 % per annum in 8 years at simple interest
Maths-General
Complete step by step solution:
Let the sum of money = P
We know the formula for total amount = A = P + SI
where A is the total amount, T is the principal amount and R is simple interest.
We know that
where P is Principal amount, T is number of years and R is rate of interest
So, …(i)
Here, we have
On substituting these values in (i), we get
On further simplifications, we get
Hence the sum of money P = Rs 285.
Maths-
The simple interest on a sum of money at the end of 3 years is of the sum itself. What rate percent was charged?
Complete step by step solution:
Let the sum of money = P
It is given that SI is times the sum itself = P.
We calculate simple interest by the formula,
where P is Principal amount, T is
number of years and R is rate of interest
Here, we have
On substituting the known values we get,
On further simplifications, we have .
The simple interest on a sum of money at the end of 3 years is of the sum itself. What rate percent was charged?
Maths-General
Complete step by step solution:
Let the sum of money = P
It is given that SI is times the sum itself = P.
We
calculate simple interest by the formula,
where P is Principal amount, T is number of years and R is rate of interest
Here, we have
On substituting the known values we get,
On further simplifications, we have .
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A graph is a geometrical representation of an equation or an expression. It can be used to find solutions of equation.
We are asked to rewrite the equation as system of equations
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Equate each side of the equation to a new variable, y:
Here we get two points where both the graphs intersect each other. The points are (-8, 0) and (-3, -7.5). Thus, we can say that the solutions to the given set of equation are the points of intersection.
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When you graph a quadratic equation find three coordinate points to get the curve. But when it is a linear equation, just two points would give
the path of the line.
Rewrite the equation as a system of equations, and then use a graph to solve.
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Hint:
A graph is a geometrical representation of an equation or an expression. It can be used to find solutions of equation.
We are asked to rewrite the equation as system of equations and graph them to solve it.
Step 1 of 3:
Equate each side of the equation to a new
variable, y:
Here we get two points where both the graphs intersect each other. The points are (-8, 0) and (-3, -7.5). Thus, we can say that the solutions to the given set of equation are the points of intersection.
Note:
When you graph a quadratic equation find three coordinate points to get the curve. But when it is a linear equation, just two points would give the path of the line.
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Rewrite the equation as a system of equations, and then use a graph to solve.
Thus, the solutions are (0, 0) and (1, -14)
Step 3 of 3:
Plot the points and join them to get the respective graph.
Here, there is just one point where both the graphs intersect each
other. The point is (4, -8). Thus, we can say that the point is the solution of the set of equation.
Note:
When you graph a quadratic equation find three coordinate points to get the curve. But when it is a linear equation, just two points would give the path of the line.
Rewrite the equation as a system of equations, and then use a graph to solve.
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Thus, the solutions are (0, 0) and (1,
-14)
Step 3 of 3:
Plot the points and join them to get the respective graph.
Here, there is just one point where both the graphs intersect each other. The point is (4, -8). Thus, we can say that the point is the solution of the set of equation.
Note:
When you graph a quadratic equation find three coordinate points to get the curve. But when it is a linear equation, just two points would give the path of the line.
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Find the simple interest on Rs. 6500 at 14% per annum for 73 days?
Complete step by step solution:
We calculate simple interest by the formula,
where P is Principal amount, T is number of years and R is rate of interest
Here, we have
On substituting the known values we get,
On further simplifications, we have rupees.
Thus,
SI = 182 Rupees.
Find the simple interest on Rs. 6500 at 14% per annum for 73 days?
Maths-General
Complete step by step solution:
We calculate simple interest by the formula,
where P is Principal amount, T is number of years and R is rate of interest
Here, we have
On substituting the known values we get,
On further simplifications, we have rupees.
Thus, SI = 182 Rupees.
Maths-
Rewrite the equation as a system of equations, and then use a graph to solve.
Here, they graphs intersect at two point; (-1 -1) and (0.5, 2). This means that the solutions of the system of equation are (-1 -1) and (0.5, 2).
Note:
Solutions of a set of
equation can be found by graphing the equations and finding the intersecting points. The points where they intersect are the solutions.
Rewrite the equation as a system of equations, and then use a graph to solve.
Maths-General
Here, they graphs intersect at two point; (-1 -1) and (0.5, 2). This means that the solutions of the system of equation are (-1 -1) and (0.5, 2).
Note:
Solutions of a set of equation can
be found by graphing the equations and finding the intersecting points. The points where they intersect are the solutions.