Question

In the beginning of the year 2004, a person invests some amount in a bank. In the beginning of 2007, the accumulated interest is Rs.10,000 and in the beginning of 2010, the accumulated interest becomes Rs.25,000. The interest rate is compounded annually and the annual interest rate is fixed. The principal amount is ​

Answer 1

Step-by-step explanation:

Given In the beginning of the year 2004, a person invests some amount in a bank. In the beginning of 2007, the accumulated interest is Rs.10,000 and in the beginning of 2010, the accumulated interest becomes Rs.25,000. The interest rate is compounded annually and the annual interest rate is fixed. The principal amount is ​

• So a person invests some amount of money in a bank in 2004. Also the accumulated interest is Rs 10,000, and in 2010 it becomes Rs 25,000, Both are compounded annually.  
• Now we need to find out the principal amount.
• So from 2004 to 2007 (beginning) for 3 years interest is Rs 10,000
• Also from 2004 to 2010(beginning) for 6 years interest is Rs 25,000
• Let the principal be m and rate of interest be 100 r%
• So Amount = p(1 + r/100)^n
•                    = m (1 + 100 r / 100)^n
•                   = m (1 + r)^n
•   Now Amount = m (1 + r)^n
• So for 3 years , A = m(1 + r)^3
•               A = P + I
•      So m(1 + r)^3 = m + 10,000
• So for 6 years we get A = m (1 + r)^6
•      So A = P + I
•     Or m(1 + r)^6 = m + 25,000
• We have both the equations  
• So m(1 + r)^3 = m + 10,000
•  So m(1 + r)^6 = m + 25,000  (m ((1 + r)^3)^2 = m + 25,000)
• Now let (1 + r)^3 = x, so we get
•   So mx = m + 10,000
• And mx^2 = m + 25,000
• Now m(x – 1) = 10,000 ------------1
• Also m(x^2 – 1) = 25,000
• So m (x - 1) (x + 1) = 25,000------2 (since a^2 – b^2 = (a + b)(a – b))
• Consider equation 1 that is m(x – 1) = 10,000
• Substituting this in equation 2 we get
• 10,000 (x + 1) = 25,000
• Or x + 1 = 25,000 / 10,000
• Or x + 1 = 2.5
• We can write x + 1 as x + 1 – 2 (since x + 1 = 2.5)
•                                   = 2.5 – 2
•                                   = 0.5
• Now from equation 1 we get m(x – 1) = 10,000
•                                            So m(0.5) = 10,000 (since x – 1 = 0.5)
•                                          Or m = 10,000 / 0.5
•                                             Or m = 20,000
• So the principal is Rs 20,000

Reference link will be

https://brainly.in/question/17703872

Answer 2

Simply equating the

AMOUNT=CI + PRINCIPAL

P(1+r/100)^t=+P

Firstly put t=3 and CI =10000

Then put t=6and CI =25000

SOLVE both the equation

As I have done below