What sum of money will amount to 9261 in 3 years at 5% per annum compound interest?

Question

What sum of money will amount to  Rs9261 in 3years at 5% per annum compound interest?

Hint:

Use the formula of total amount to find the principal amount.

The correct answer is: 8000 Rupees

Complete step by step solution:Let the principal amount = PHere we have R = 5% , T = 3 years and total amount A = 9261 Rupees.We know that …(i)On substituting the known values in (i), we get  Rupees.Hence the principal amount P = 8000 Rupees.

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Related Questions to study

Maths-

Dubey borrows  Rs 1,00,000 from the State Bank of India at 11% p.a. compound interest. He repays Rs 41,000 at the end of the first year and  Rs47,700 at the end of the second year. Find the am not outstanding at the beginning of the third year. 

Complete step by step solution:
Money borrowed by Dubey at 11% compound interest, that is  = Rs 100000
For first year,
We know that compound interest = Total amount - principal amount that is, CI = A - P…(i)
Here we have …(ii)
Here, we have T = 1 years, P = 100000 , R = 11% and A = ?
On substituting the known values in (ii), we get 
On substituting the known values in (i), we get

 Rs
Thus total amount after 1 year = 100000 + 11000 = 111000 Rupees.
Money repaid = Rs 41000
∴ Balance = 111000 - 41000 = 70000 Rupees.
For second year,
Here, we have T = 1  years, P = 70000 , R = 11% and A = ?
On substituting the known values in (ii), we get 
On substituting the known values in (i), we get

 Rs
Thus total amount after 1 year = 70000 + 7700 = 77700 Rupees.
Money paid at the end of second year by Dubey = Rs 47700
∴ Loan at the beginning of third year = 777000 - 47700 = Rs 30000

Dubey borrows  Rs 1,00,000 from the State Bank of India at 11% p.a. compound interest. He repays Rs 41,000 at the end of the first year and  Rs47,700 at the end of the second year. Find the am not outstanding at the beginning of the third year. 

Maths-General

Complete step by step solution:
Money borrowed by Dubey at 11% compound interest, that is  = Rs 100000
For first year,
We know that compound interest = Total amount - principal amount that is, CI = A - P…(i)
Here we have …(ii)
Here, we have T = 1 years, P = 100000 , R = 11% and A = ?
On substituting the known values in (ii), we get 
On substituting the known values in (i), we get

 Rs
Thus total amount after 1 year = 100000 + 11000 = 111000 Rupees.
Money repaid = Rs 41000
∴ Balance = 111000 - 41000 = 70000 Rupees.
For second year,
Here, we have T = 1  years, P = 70000 , R = 11% and A = ?
On substituting the known values in (ii), we get 
On substituting the known values in (i), we get

 Rs
Thus total amount after 1 year = 70000 + 7700 = 77700 Rupees.
Money paid at the end of second year by Dubey = Rs 47700
∴ Loan at the beginning of third year = 777000 - 47700 = Rs 30000

Maths-

Nikita invests  Rs6000 for two years at a certain rate of interest compounded annually. At the end of the 1st year, it amounts to Rs6720. Calculate (i). the rate of interest (ii) the amount at the end of 2nd year 

Complete step by step solution:
Let the rate of interest = R
(i)  We know that …(i)
Here, we have T = 1 year, P = 6000, A = 6720 and R = ?
On substituting the known values in (i), we get 
On dividing both the sides by 6000, we have

(ii) We know that …(ii)
Here, we have T = 2 years, P = 6000, R = 12
Amount at the end of second year will be,
On substituting the known values in (ii), we get

 Rupees
So the amount to be paid at the end of 2 years = 7526.4 Rupees.

Nikita invests  Rs6000 for two years at a certain rate of interest compounded annually. At the end of the 1st year, it amounts to Rs6720. Calculate (i). the rate of interest (ii) the amount at the end of 2nd year 

Maths-General

Complete step by step solution:
Let the rate of interest = R
(i)  We know that …(i)
Here, we have T = 1 year, P = 6000, A = 6720 and R = ?
On substituting the known values in (i), we get 
On dividing both the sides by 6000, we have

(ii) We know that …(ii)
Here, we have T = 2 years, P = 6000, R = 12
Amount at the end of second year will be,
On substituting the known values in (ii), we get

 Rupees
So the amount to be paid at the end of 2 years = 7526.4 Rupees.

Maths-

Rohit borrows  Rs86,000 from Arun for two years at 5% per annum simple interest. He immediately lends out this money to Akshay at 5% compound interest compounded annually for the same period. Calculate Rohit’s profit in the transaction at the end of two years.

Complete step by step solution:
Case I
Money borrowed from Arun by Rohith = P = 86000 Rupees.
Here we have rate of simple interest R = 5% and number of years T = 2 years.
Interest to be paid by Rohith,
We calculate simple interest by the formula,…(i)
where P is Principal amount, T is number of years and R is rate of interest
On substituting the known values in (i), we get  Rupees.
Amount at the end of 2 years = 86000 + 8600 = 94600 Rupees.
Case II
Let the principal amount = P
Here we have rate of simple interest R = 5% and number of years T = 2 years.
We know that 
Amount to be paid by Akshay,
So, total amount after second year = 
 Rupees.
∴Rohith’s profit = 94815 - 94600 = 215 Rupees

Rohit borrows  Rs86,000 from Arun for two years at 5% per annum simple interest. He immediately lends out this money to Akshay at 5% compound interest compounded annually for the same period. Calculate Rohit’s profit in the transaction at the end of two years.

Maths-General

Complete step by step solution:
Case I
Money borrowed from Arun by Rohith = P = 86000 Rupees.
Here we have rate of simple interest R = 5% and number of years T = 2 years.
Interest to be paid by Rohith,
We calculate simple interest by the formula,…(i)
where P is Principal amount, T is number of years and R is rate of interest
On substituting the known values in (i), we get  Rupees.
Amount at the end of 2 years = 86000 + 8600 = 94600 Rupees.
Case II
Let the principal amount = P
Here we have rate of simple interest R = 5% and number of years T = 2 years.
We know that 
Amount to be paid by Akshay,
So, total amount after second year = 
 Rupees.
∴Rohith’s profit = 94815 - 94600 = 215 Rupees

Maths-

Kamal borrowed  Rs 15,000 for two years. The rate of interest for two successive years is 8% and 10% respectively. If he repays  Rs 6200 at the end of the first year, find the outstanding amount at the end of the second year.

SOLUTION:
HINT: Find the total amount at first year, then subtract the repaid amount and then find the amount
to be paid at the end of second year.
Complete step by step solution:
For first year,
Let the money borrowed by Kamal be the principal amount, P1 = 15000 Rupees
Here we have rate of interest R = 8% number of years T = 1
We know that 
So, total amount after one year = 
 Rupees.
Money repaid at the end of first year = 6200 Rupees.
∴ Balance = 16200 - 6200 = 10000 Rupees.
For second year,
The principal amount becomes P2 = 10000 Rupees.
Here we have rate of interest R = 10% number of years T = 1
We know that 
So. total amount after second year = 
 Rupees.
Hence the amount to be paid at the end of second year = 11000 Rupees.

Kamal borrowed  Rs 15,000 for two years. The rate of interest for two successive years is 8% and 10% respectively. If he repays  Rs 6200 at the end of the first year, find the outstanding amount at the end of the second year.

Maths-General

SOLUTION:
HINT: Find the total amount at first year, then subtract the repaid amount and then find the amount
to be paid at the end of second year.
Complete step by step solution:
For first year,
Let the money borrowed by Kamal be the principal amount, P1 = 15000 Rupees
Here we have rate of interest R = 8% number of years T = 1
We know that 
So, total amount after one year = 
 Rupees.
Money repaid at the end of first year = 6200 Rupees.
∴ Balance = 16200 - 6200 = 10000 Rupees.
For second year,
The principal amount becomes P2 = 10000 Rupees.
Here we have rate of interest R = 10% number of years T = 1
We know that 
So. total amount after second year = 
 Rupees.
Hence the amount to be paid at the end of second year = 11000 Rupees.

Maths-

In what period will  Rs 12,000 yields Rs3,972 as compound interest at 10% per annum; if compounded every year.

Complete step by step solution:
We know that compound interest = Total amount - principal amount that is, CI = A - P…(i)
We know that  …(ii)
Here, we have T = ? years, P = 12000 and R = 10%
On substituting the known values in (ii), we get 
Given that CI = 3972,
On substituting the known values in (i), we get 
On adding 12000 on both the sides, we have 
Divide on both sides by 12000.
On dividing we have,

T = 3 years.
In 3 years, Rs 12000 yields 3972 as compound interest at 10% per annum if compounded every Year.

In what period will  Rs 12,000 yields Rs3,972 as compound interest at 10% per annum; if compounded every year.

Maths-General

Complete step by step solution:
We know that compound interest = Total amount - principal amount that is, CI = A - P…(i)
We know that  …(ii)
Here, we have T = ? years, P = 12000 and R = 10%
On substituting the known values in (ii), we get 
Given that CI = 3972,
On substituting the known values in (i), we get 
On adding 12000 on both the sides, we have 
Divide on both sides by 12000.
On dividing we have,

T = 3 years.
In 3 years, Rs 12000 yields 3972 as compound interest at 10% per annum if compounded every Year.

Maths-

On what sum of money will the difference between the compound interest and simple interest for 2years be equal to Rs 25 if the rate of interest charged for both is 5% p.a. 

Complete step by step solution:
Let the principal amount = P
It is given that the rate of interest R = 5% and number of years T = 2 years.
So, compound interest for 2 years = 
Simple  interest for 2 years = 
It is given that compound interest - simple interest = 25 Rupees
That is,

 Rupees.
Hence the principal amount = Rs 10000

On what sum of money will the difference between the compound interest and simple interest for 2years be equal to Rs 25 if the rate of interest charged for both is 5% p.a. 

Maths-General

Complete step by step solution:
Let the principal amount = P
It is given that the rate of interest R = 5% and number of years T = 2 years.
So, compound interest for 2 years = 
Simple  interest for 2 years = 
It is given that compound interest - simple interest = 25 Rupees
That is,

 Rupees.
Hence the principal amount = Rs 10000

Maths-

At what rate % p.a will a sum of  Rs4000 yield 1324 as compound interest in 3 yrs 

Complete step by step solution:
We know that compound interest = Total amount - principal amount that is, CI = A - P …(i)
We know that …(ii)
Here, we have T = 3 years, P = 4000 and    R = ?
On substituting the known values in (ii), we get 
Given that CI = 1324,
On substituting the known values in (i), we get 
On adding 4000 on both the sides, we have 
Divide on both sides by 4000.
On dividing we have,

So, at 10% pa per annum will a sum of Rs 4000 yield 1324 as compound interest in 3 years.

At what rate % p.a will a sum of  Rs4000 yield 1324 as compound interest in 3 yrs 

Maths-General

Complete step by step solution:
We know that compound interest = Total amount - principal amount that is, CI = A - P …(i)
We know that …(ii)
Here, we have T = 3 years, P = 4000 and    R = ?
On substituting the known values in (ii), we get 
Given that CI = 1324,
On substituting the known values in (i), we get 
On adding 4000 on both the sides, we have 
Divide on both sides by 4000.
On dividing we have,

So, at 10% pa per annum will a sum of Rs 4000 yield 1324 as compound interest in 3 years.

Maths-

The compound interest, calculated yearly, on a certain sum of money for the second year is Rs1320 and for the third year is Rs1452. Calculate the rate of interest and the original sum of money.

Complete step by step solution:
Compound interest for third year = Rs 1452 Rupees
Compound interest for second year = Rs 1320 Rupees
So, difference = 1452 - 1320 = 132 Rupees.
Hence interest for third year = Rs 132 (simple interest and compound interest for 1 year is same)
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 SI = 132,P = 1320 ,T = 1 and R = ?
On substituting the known values in (i), we get

Let the principal amount = P
Amount after 1st year - Amount after 2nd year = Rs 1320

 Rs
Hence rate of interest is 10% and original money is 12000 Rupees.

The compound interest, calculated yearly, on a certain sum of money for the second year is Rs1320 and for the third year is Rs1452. Calculate the rate of interest and the original sum of money.

Maths-General

Complete step by step solution:
Compound interest for third year = Rs 1452 Rupees
Compound interest for second year = Rs 1320 Rupees
So, difference = 1452 - 1320 = 132 Rupees.
Hence interest for third year = Rs 132 (simple interest and compound interest for 1 year is same)
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 SI = 132,P = 1320 ,T = 1 and R = ?
On substituting the known values in (i), we get

Let the principal amount = P
Amount after 1st year - Amount after 2nd year = Rs 1320

 Rs
Hence rate of interest is 10% and original money is 12000 Rupees.

Maths-

Ranbir borrows  Rs20,000 at 12% per annum compound interest. If he repays  Rs8400 at the end of the first year and  Rs9680 at the end of the second year. Find the amount of loan outstanding at the beginning of the third year.

Complete step by step solution:
Money borrowed by Ranbir at 12% compound interest, that is  = Rs 20000
For first year,
We know that compound interest = Total amount - principal amount that is, CI = A - P …(i)
Here we have …(ii)
Here, we have T = 1 years, P = 20000 , R = 12% and A = ?
On substituting the known values in (ii), we get 
On substituting the known values in (i), we get

 Rs
Thus total amount after 1 year = 20000+2400=22400 Rupees.
Money repaid = Rs 8400
∴ Balance = 22400 - 8400 = 14000 Rupees.
For second year,
Here, we have T = 1 years, P = 14000 , R = 12% and A = ?
On substituting the known values in (ii), we get 
On substituting the known values in (i), we get 
 Rs
Thus total amount after 1 year = 14000+1680=15680 Rupees.
Money paid at the end of second year by Ranbir = Rs 9680
∴ Loan at the beginning of third year = 15680 - 9680 = Rs 6000

Ranbir borrows  Rs20,000 at 12% per annum compound interest. If he repays  Rs8400 at the end of the first year and  Rs9680 at the end of the second year. Find the amount of loan outstanding at the beginning of the third year.

Maths-General

Complete step by step solution:
Money borrowed by Ranbir at 12% compound interest, that is  = Rs 20000
For first year,
We know that compound interest = Total amount - principal amount that is, CI = A - P …(i)
Here we have …(ii)
Here, we have T = 1 years, P = 20000 , R = 12% and A = ?
On substituting the known values in (ii), we get 
On substituting the known values in (i), we get

 Rs
Thus total amount after 1 year = 20000+2400=22400 Rupees.
Money repaid = Rs 8400
∴ Balance = 22400 - 8400 = 14000 Rupees.
For second year,
Here, we have T = 1 years, P = 14000 , R = 12% and A = ?
On substituting the known values in (ii), we get 
On substituting the known values in (i), we get 
 Rs
Thus total amount after 1 year = 14000+1680=15680 Rupees.
Money paid at the end of second year by Ranbir = Rs 9680
∴ Loan at the beginning of third year = 15680 - 9680 = Rs 6000

Maths-

The present population of a town is 200000. Its population increases by 10% in the first year and 15% in the second year. Find the population of the town at the end of the two years.

Complete step by step solution:
Present population of the town P = 200000,
We calculate the total population at the end of first year by the formula …(i)
Here, we have T = 1 years, P = 200000 ,R = 10% and A = ?
On substituting the known values in (i), we get

Hence total population at the end of first year = 220000
So the new population is 220000
Now the formula to find total population at the end of two years =  …(ii)
Here, we have T = 1 years, P = 220000 , R = 15%(increases) and A = ?
On substituting the known values in (ii), we get

Hence total population at the end of second year = 253000

The present population of a town is 200000. Its population increases by 10% in the first year and 15% in the second year. Find the population of the town at the end of the two years.

Maths-General

Complete step by step solution:
Present population of the town P = 200000,
We calculate the total population at the end of first year by the formula …(i)
Here, we have T = 1 years, P = 200000 ,R = 10% and A = ?
On substituting the known values in (i), we get

Hence total population at the end of first year = 220000
So the new population is 220000
Now the formula to find total population at the end of two years =  …(ii)
Here, we have T = 1 years, P = 220000 , R = 15%(increases) and A = ?
On substituting the known values in (ii), we get

Hence total population at the end of second year = 253000

Maths-

In what time will Rs1500 yield  Rs1996.50 as compound interest at 10% per annum compounded annually? 

Complete step by step solution:
We calculate the total amount by the formula …(i)
where P is Principal amount, T is number of years and R is rate of interest
Here, we have R = 10% ,P = 1500 , A = 1996.5 and T = ?
On substituting the known values in (i), we get 
On dividing both the sides by 1500, we have

T = 3 years
In 3 years will Rs 1500 yield Rs 1996.50 as compound interest at 10% per annum compounded annually.

In what time will Rs1500 yield  Rs1996.50 as compound interest at 10% per annum compounded annually? 

Maths-General

Complete step by step solution:
We calculate the total amount by the formula …(i)
where P is Principal amount, T is number of years and R is rate of interest
Here, we have R = 10% ,P = 1500 , A = 1996.5 and T = ?
On substituting the known values in (i), we get 
On dividing both the sides by 1500, we have

T = 3 years
In 3 years will Rs 1500 yield Rs 1996.50 as compound interest at 10% per annum compounded annually.

Maths-

Mr. utter invested  Rs5000 at a certain rate of interest, compounded annually for two years. At the end of the first year, it amounts to  Rs5325. Calculate (i) The rate of interest (ii) The amount at the end of the second year, to the nearest rupee.

Complete step by step solution:
(i) We calculate the total amount by the formula …(i)
where P is Principal amount, T is number of years and R is rate of interest
Here, we have T = 1 years, P = 500, A = 5325 and R = ?
On substituting the known values in (i), we get 
On dividing both the sides by 5000, we have 1.065 =

(ii) By the end of first year principal amount becomes, P = 5325 Rupees
We calculate amount at the end of second year by the formula …(ii)
Here, we have T = 1 years, P = 5325, R = 6.5 and A = ?
On substituting the known values in (ii), we get

 Rupees(approx)
Hence the amount at end of second year = 5671 Rupees

Mr. utter invested  Rs5000 at a certain rate of interest, compounded annually for two years. At the end of the first year, it amounts to  Rs5325. Calculate (i) The rate of interest (ii) The amount at the end of the second year, to the nearest rupee.

Maths-General

Complete step by step solution:
(i) We calculate the total amount by the formula …(i)
where P is Principal amount, T is number of years and R is rate of interest
Here, we have T = 1 years, P = 500, A = 5325 and R = ?
On substituting the known values in (i), we get 
On dividing both the sides by 5000, we have 1.065 =

(ii) By the end of first year principal amount becomes, P = 5325 Rupees
We calculate amount at the end of second year by the formula …(ii)
Here, we have T = 1 years, P = 5325, R = 6.5 and A = ?
On substituting the known values in (ii), we get

 Rupees(approx)
Hence the amount at end of second year = 5671 Rupees

Maths-

On a certain sum of money, the difference between the compound interest for a year payable half-yearly and the simple interest for a year is  16. Find the sum lent out; if the rate of interest in both cases is 8%.

Complete step by step solution:
Let the sum of money = P
It is given that rate of interest R = 8% and number of years T = 1
Also Compound interest - Simple interest = CI - SI  = Rs 16
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 = 1 years, R = 8%  and P = ?
On substituting the known values in (i), we get …(ii)
We calculate compound interest by the formula …(iii) payable half yearly
where P is Principal amount, T is number of years and R is rate of interest
Here, we have T = 1,R = 8% and P = ?
On substituting the known values in (iii), we get

…(iv)
We have 
On further simplifications, we have

Hence the sum of money P = 10000 Rupees.

On a certain sum of money, the difference between the compound interest for a year payable half-yearly and the simple interest for a year is  16. Find the sum lent out; if the rate of interest in both cases is 8%.

Maths-General

Complete step by step solution:
Let the sum of money = P
It is given that rate of interest R = 8% and number of years T = 1
Also Compound interest - Simple interest = CI - SI  = Rs 16
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 = 1 years, R = 8%  and P = ?
On substituting the known values in (i), we get …(ii)
We calculate compound interest by the formula …(iii) payable half yearly
where P is Principal amount, T is number of years and R is rate of interest
Here, we have T = 1,R = 8% and P = ?
On substituting the known values in (iii), we get

…(iv)
We have 
On further simplifications, we have

Hence the sum of money P = 10000 Rupees.

Maths-

A   person invests  Rs6000 at 14% interest for 2 years. Calculate(i) the interest for the 1st year(ii)   the amount at the end of the first year(iii) the interest for the second year.

Complete step by step solution:
(i) We calculate simple interest by the formula,…(i)
where P is Principal amount, T is number of years and R is rate of interest
Let the sum of money P = 6000 Rs
Here, we have T = 1 years, R = 14% and P = 6000 Rs
On substituting the known values in (i), we get

We have SI = 840 Rupees as the interest for 1st year.
(ii)  Formula for total amount = A = P + SI,
where A is the total amount, P is the principal amount and SI is simple interest .
We have P = 6000 and SI = 840.
On substitution, we get A = 6000 + 840 = 6840 Rupees.
The amount at the end of first year = 6840 Rupees.
(iii) By the end of first year principal amount becomes, P = 6840 Rupees
We calculate simple interest for the second year by the formula …(i)
where P is Principal amount, T is number of years and R is rate of interest
Let the sum of money P = 6840 Rs
Here, we have T = 1 years, R = 14% and P = 6840 Rs
On substituting the known values in (i), we get

We have SI = 957.6 Rupees as the interest for 2nd year.
Hence option C is the correct answer.

A   person invests  Rs6000 at 14% interest for 2 years. Calculate(i) the interest for the 1st year(ii)   the amount at the end of the first year(iii) the interest for the second year.

Maths-General

Complete step by step solution:
(i) We calculate simple interest by the formula,…(i)
where P is Principal amount, T is number of years and R is rate of interest
Let the sum of money P = 6000 Rs
Here, we have T = 1 years, R = 14% and P = 6000 Rs
On substituting the known values in (i), we get

We have SI = 840 Rupees as the interest for 1st year.
(ii)  Formula for total amount = A = P + SI,
where A is the total amount, P is the principal amount and SI is simple interest .
We have P = 6000 and SI = 840.
On substitution, we get A = 6000 + 840 = 6840 Rupees.
The amount at the end of first year = 6840 Rupees.
(iii) By the end of first year principal amount becomes, P = 6840 Rupees
We calculate simple interest for the second year by the formula …(i)
where P is Principal amount, T is number of years and R is rate of interest
Let the sum of money P = 6840 Rs
Here, we have T = 1 years, R = 14% and P = 6840 Rs
On substituting the known values in (i), we get

We have SI = 957.6 Rupees as the interest for 2nd year.
Hence option C is the correct answer.

Maths-

At what percent by simple interest will a sum of money double itself in 5 years 4 months?

Complete step by step solution:
Formula for total amount = A = P + SI…(i)
where A is the total amount, P is the principal amount and SI is simple interest .
Here, A = 2P and SI = 
where P is Principal amount, T is number of years and R is the rate of interest.
We have, T = 5 years and 4 months =  years (given) and R = ?
On substituting the known values in (i), we have .
Subtract P from both sides.
Then we have,

So, we have R = 18.75%
At 18.75% per annum the sum amount will double itself in 5 years and 4 months.

At what percent by simple interest will a sum of money double itself in 5 years 4 months?

Maths-General

Complete step by step solution:
Formula for total amount = A = P + SI…(i)
where A is the total amount, P is the principal amount and SI is simple interest .
Here, A = 2P and SI = 
where P is Principal amount, T is number of years and R is the rate of interest.
We have, T = 5 years and 4 months =  years (given) and R = ?
On substituting the known values in (i), we have .
Subtract P from both sides.
Then we have,

So, we have R = 18.75%
At 18.75% per annum the sum amount will double itself in 5 years and 4 months.

What sum of money will amount to Rs 9261 in 3 years at 5% per annum compound annually?

What sum of money will amount to Rs 3704.40 in 3 years at 5% compound interest?

On what sum will compound interest of 5% pa?

On what sum of money will compound interest for 2 years at 5% per annum amounts to rupees 164?