Question

Mr. Dua invested money in two schemes a and b offering compound interest @8p.C.P.A and 9 p.C.P.A respectively. If the total amount of interest accrued through two schemes together in two years was rs.4828.30 and the total amount invested was rs.27000. What was the amount invested in scheme a?

Answer 1

Let the Amount of Money Invested in Scheme 'a' be : A

Given : The Total Amount of Money invested by Dua = Rs. 27000

⇒ The Amount of Money Invested in Scheme 'b' = 27000 - A

Given : The Rate of Interest for Scheme 'a' = 8%

We know that : Amount in Compound Interest is given by :

$\clubsuit\;\;Amount = P(1 + \frac{R}{100})^n$

Where :

$\spadesuit$  P is the Principal

$\spadesuit$  R is the Rate of Interest

$\spadesuit$  n is the Total Number of Conversion Periods

Let us Find the Interest Obtained by Dua by Investing in Scheme 'a' :

Here : Principal(P) = A and Rate of Interest (R) = 8 and n = 2, Because we are compounding annually and Calculating the Amount after 2 years of Investment.

$\implies Amount = A(1 + \frac{8}{100})^2\\\\\implies Amount = A(1 + 0.08)^2\\\\\implies Amount = A(1.08)^2$

Interest obtained by Investing Scheme 'a' = A(1.08)² - A = A[(1.08)² - 1]

Let us Find the Interest Obtained by Dua by Investing in Scheme 'b' :

Here : Principal(P) = 27000 - A and Rate of Interest (R) = 9 and n = 2, Because we are compounding annually and Calculating the Amount after 2 years of Investment.

$\implies Amount = (27000 - A)(1 + \frac{9}{100})^2\\ \\\implies Amount = (27000 - A)(1 + 0.09)^2\\\\\implies Amount = (27000 - A)(1.09)^2$

⇒ Interest Obtained by Investing in Scheme 'b' :

⇒ (27000 - A)(1.09)² - (27000 - A)

⇒ (27000 - A)[(1.09)² - 1]

Given : Total Interest Dua received in Two Schemes = 4828.30

⇒ (27000 - A)[(1.09)² - 1] + A[(1.08)² - 1] = 4828.30

⇒ (27000 - A)(0.1881) + A(0.1664) = 4828.30

⇒ (27000 × 0.1881) - 0.1881A + 0.1664A = 4828.30

⇒ 5078.7 - 0.0217A = 4828.30

⇒ 0.0217A = 5078.7 - 4828.30

⇒ 0.0217A = 250.4

⇒ A = 11539.17 Rs

⇒ Amount Invested in Scheme 'a' is 11539.17 Rs

Answer 2

Hence The Answer is

$\bold \red{Rs \: 12, 00}$