Question

Solution for total of `8,600 was invested in two accounts. One account earned 4 3 4 % annual interest and the other earned 6 1 2 % annual interest. If the total interest for one year was ₹431.25, how much was invested in each account? (use determinant method).

Answer 1

Answer:

Rs 7300 and Rs 1300

Step-by-step explanation:

Compound interest formula is given by :

C.I = P[(1 + r)ⁿ - 1]

Where :

P = initial amount

r = interest rate

n = time in years

Let one of the principles be x and the other principle be 8600 - x

Doing the substitution we have :

r = 4.75%

CI = x[(1.0475) - 1] = 0.0475x

r = 6.5%

CI = 8600 - x[(1.065) - 1]

CI = (8600 - x) × 0.065 = 559 - 0.065x

The total interest is :

559 - 0.065x + 0.0475x = 431.25

559 - 0.0175x = 431.25

-0.0175x = 431.25 - 559

-0.0175x = - 127.75

x = 127.75/0.0175

x = 7300

In the first account with an interest of 4.75% rs 7300 was invested.

In the second account with a rate of 6.5% rs (8600 - 7300) = 1300 was invested.