He invested $6,000 in the account paying 5% and $18,500 in the account paying 7%
Step-by-step explanation:
The formula of the interest is I = Prt, where
- P is the money invested
- r is the rate of interest in decimal
- t is the time of investment
Alexis invests $24,500 in two accounts paying 5% and 7% annual
interest. After one year, the total interest was $1,595
Assume that he invested $
in the account paying 5% annual interest and $
in the account paying 7% annual interest
∵ The investment in the account paying 5% is $ ![P_{1}](https://tex.z-dn.net/?f=P_%7B1%7D)
∵ The investment in the account paying 7% is $ ![P_{2}](https://tex.z-dn.net/?f=P_%7B2%7D)
∵ He invests $24,500 in both accounts
∴
+
= 24,500 ⇒ (1)
∵
=
t
∵
= 5% = (5/100) = 0.05
∵ t = 1
∴
=
(0.05)(1)
∴
= 0.05 ![P_{1}](https://tex.z-dn.net/?f=P_%7B1%7D)
∵
=
t
∵
= 7% = (7/100) = 0.07
∵ t = 1
∴
=
(0.07)(1)
∴
= 0.07 ![P_{2}](https://tex.z-dn.net/?f=P_%7B2%7D)
∵ The total interest is $1,595
∴
+
= 1,595
- Substitute the value of
and
in the equation
∴ 0.05
+ 0.07
= 1,595 ⇒ (2)
Now let us solve the system of the equations
Multiply equation (1) by -0.07 to eliminate ![P_{2}](https://tex.z-dn.net/?f=P_%7B2%7D)
∴ - 0.07
- 0.07
= - 1715 ⇒ (3)
- Add equations (2) and (3)
∴ - 0.02
= - 120
- Divide both sides by - 0.02
∴
= 6000
∴ He invested $6,000 in the account paying 5%
Substitute the value of
in equation (1) to find ![P_{2}](https://tex.z-dn.net/?f=P_%7B2%7D)
∵ 6000 +
= 24,500
- Subtract 6000 from both sides
∴
= 18500
∴ He invested $18,500 in the account paying 7%
He invested $6,000 in the account paying 5% and $18,500 in the account paying 7%
Learn more:
You can learn more about interest in brainly.com/question/10672611
#LearnwithBrainly