Question

divide rs 21000 into two parts so that the amount of first part for 2 years is same as the amount of second part for 3 years at the rate of 10%p.a. compounded annually​

Answer 1

Let's assume that the two parts into which Rs.
41,000 is divided are x and y. Now, we know that the interest is compounded annually at a rate of 50% per annum. Therefore, the amount after 2 years will be (x* (1 + 0.5) ^2) and the amount after 3 years will be (y * (1 + 0.5) ^3).We also know that the amounts after 2 years and 3 years are equal.
Therefore, we can set up the following equation:x *
(1 + 0.5) ^2 = y * (1 + 0.5)^ 3Simplifying this
equation, we get: *1.5^2 = y* 1.5^3х* 2.25 = y*
3.375x/y = 3/2Using this relationship, we can solve
for x and y as follows: + y = 41,000x/y =
3/Substituting x/y = 3/2, we get: = (3/5) * 41,000
= 24,600y = (2/5) * 41,000 = 16,400Therefore, the
two parts into which Rs. 41,000 should be divided are Rs. 24,600 and Rs. 16,400, respectively.

Answer 2

To divide Rs 21000 into two parts that obtain the same compound interest amount over different time periods at 10% p.a., set up an equation comparing the compound interest formula for both parts and solve for the principal amounts.

Step-by-step explanation:

The student has asked to divide Rs 21000 into two parts such that the amount of the first part for 2 years is the same as the amount of the second part for 3 years, with both earning compound interest at an annual rate of 10%. To solve this, we can set up an equation based on the formula for compound interest:

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

Where A is the amount of money accumulated after n years, including interest, P is the principal amount, r is the annual interest rate, n is the number of times that interest is compounded per year, and t is the time the money is invested for. Given that both amounts after the said periods are equal, we can equate them as follows:

Part1(1 + 0.10)2 = Part2(1 + 0.10)3

Since the total is Rs 21000, Part1 + Part2 = 21000. We can solve these equations simultaneously to find the values of Part1 and Part2. By doing the math, we can find the correct division of the total sum into two parts that meet the given condition.