Question

Larry Mitchell invested part of gis 35,000 advance at 3% annual simple interest and the rest at 2% annual simple interest. If his total yearly interest from both accounts was $900, find the amount invested at each rate.

Answer 1

Answer:

He invested $20000 for 3% rate and $15000 for 2% rate.

Step-by-step explanation:.

Let the 3% rate be for Account A and the 2% rate for Account B.

From the question, we know that the Principal from both accounts must add up to $35000

$P_A + P_B =$ 35000 ________________________ (1)

We also know that the interest from both accounts add up to $900

$I_A + I_B = 900$________________________(2)

The Interest from Account A (R = 3%, T = 1) is:

$I_A = \frac{P_A *R*T}{100}$

This implies that:

$I_A = \frac{P_A *3*1}{100}\\\\\\I_A = \frac{3P_A}{100} \\\\\\100*I_A = 3P_A\\\\\\100I_A - 3P_A = 0$________________________(3)

The Interest from Account B (R = 2%, T = 1) is:

$I_B = \frac{P_B *R*T}{100}$

This implies that:

$I_B = \frac{P_B *2*1}{100}\\\\\\I_B = \frac{2P_B}{100} \\\\\\100*I_B = 2P_B\\\\\\100I_B - 2P_B = 0$_____________________________(4)

From (1),

$P_B = 35000 - P_A$

Putting this in (4)

$100I_B - 2*(35000 - P_A) = 0\\\\100I_B -70000 + 2P_A = 0\\\\100I_B +2P_A = 70000$________________(5)

From (2):

$I_A = 900 - I_B$

Putting this in (3):

$100(900 - I_B) - 3P_A = 0\\\\90000 - 100I_B - 3P_A = 0\\\\100I_B +3P_A = 90000$_______________________(6)

(5) and (6) are simultaneous equations, hence, we can solve them:

$100I_B +3P_A = 90000\\\\100I_B + 2P_A = 70000$

Subtracting (5) from (6):

$3P_A - 2P_A = 90000 - 70000$

$P_A =$ $20000

Hence:

$P_B = 35000 - 20000$

$P_B =$ $15000

Also:

$100I_B + 3P_A = 90000\\\\100I_B + (3 * 20000) = 90000\\\\100I_B + 60000 = 90000\\\\\\100I_B = 90000 - 60000\\\\100I_B = 30000$

$I_B = 3000/100$ = $300

Hence:

$I_A = 900 - 300$

$I_A =$ $600

Hence, Larry invested $20000 at 3% annual interest and got $600 interest. He also invested $15000 at 2% annual interest and got $300.