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).
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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.
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