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A bank loaned out $20,000, part of it at the rate of 9% per year and the rest at 17% per
year. If the interest received in one year totaled $3000, how much was loaned at 9%?
How much of the $20,000 did the bank loan out at 9%?

Respuesta :

Answer:

The bank loan out at $5000 at 9%

Step-by-step explanation:

A bank loaned out $20,000

Let x be the amount loaned at at the rate of 9% per year

So, 20000-x amount loaned at at the rate of 17% per year

Formula : [tex]A =P(1+r)^t[/tex]

Amount at 9% interest in 1 year

[tex]A=x(1+0.09)^1[/tex]

A=1.09x

Interest = Amount - Principal = 1.09x-x=0.09x

Amount at 17% interest in 1 year

[tex]A=(20000-x)(1+0.17)^1[/tex]

A=1.17(20000-x)

Interest = Amount - Principal = 1.17(20000-x)-(20000-x)

We are given that the interest received in one year totaled $3000

So,1.17(20000-x)-(20000-x)+0.09x=3000

x=5000

So, the bank loan out at $5000 at 9%