Question

Marco has $8,000 to save for his daughter’s college education. He wants to divide it between Account A, which pays 3.2% interest per year, and Account B, which pays 8% interest per year. How much should he invest in each account if he wants the interest on the total investment to be 6.5%?

Answer 1

Answer: In account A = $ 2,500

In account B = $ 5,500

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

=
`x ( 1 + (3.2)/(100))^1`

= x ( 1 + 0.032 )

= x (1.032)

Similarly, Account B pays 8% interest per year,

Thus, the total amount by B after a year

=
`(8000-x) ( 1 + (8)/(100))^1`

= (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