Respuesta :
Answer: In account A = $ 2,500
In account B = $ 5,500
Step-by-step explanation:
Here, total investment = $ 8000
Let he invested x dollars in Account A,
⇒ His investment in account B = ( 8000 - x ) dollars
Since, Account A pays 3.2% interest per year,
Thus, the total amount by A after a year
= [tex]x ( 1 + \frac{3.2}{100})^1[/tex]
= x ( 1 + 0.032 )
= x (1.032)
Similarly, Account B pays 8% interest per year,
Thus, the total amount by B after a year
= [tex](8000-x) ( 1 + \frac{8}{100})^1[/tex]
= (8000-x) ( 1 + 0.080 )
= (8000-x) (1.08)
Hence, the total amount by both account = x(1.032)+(8000-x)(1.08)
But, According to the question,
he wants the interest on the total investment to be 6.5%
Thus, the amount he want after one year by both accounts
= 8000 (1+0.065) = 8000 (1.065)
⇒ x (1.032) + (8000-x) (1.08)=8000 (1.065)
⇒ 1.032 x + 8000×1.08 - 1.08 x = 8000× 1.065
⇒ −0.048 x + 8640 = 8520
⇒ - 0.048 x = - 120
⇒ x = 2500
Hence, Investment in account A = x = $ 2500
And, Investment in account B = 8000 - x = 8000- 2500 = $ 5500
