Question

A $5,000 principal is invested in two accounts, one earning 1% interest and another earning 6% interest. If the total interest for the year is $170, then how much is invested in each account?

Answer 1

Answer:

$2600 was invested on the 1% account while $2400 was invested on the 6% account.

Step-by-step explanation:

For simple interest we must apply the following formula:

M = C*r*t

Where M is the amount of interest generated, C is the invested money, r is the rate of interest and t is the elapsed time.

The sum of capital investead in each account, "x" for the 1% interest one and "y" for the 6% interest one, must be equal to the original $5000. The same way as the interest generated from these investments must be equal to the earnt $170. So we have:

x + y = 5000

For the first account:

M1 = x*0.01*1 = 0.01*x

For the second account:

M2 = y*0.06*1 = 0.06*y

The sum of interests:

0.01*x + 0.06*y = 170

We have a system of equations as shown below:

x + y = 5000

0.01*x + 0.06*y = 170

Multiplying the first equation by -0.01 and adding both equations we have:

-0.01*x - 0.01*y = -50

0.01*x + 0.06*y = 170

0.05*y = 120

y = 120 / 0.05 = $2400

x = 5000 - 2400 = $2600

$2600 was invested on the 1% account while $2400 was invested on the 6% account.