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juin [17]
3 years ago
8

Last year, Keiko had $20,000 to invest. She invested some of it in an account that paid %7 simple interest per year, and she inv

ested the rest in an account that paid %5 simple interest per year. After one year, she received a total of $1,280 in interest. How much did she invest in each account?
Mathematics
1 answer:
erma4kov [3.2K]3 years ago
4 0

Answer:

P_2 = \$6,000\\P_1 = \$14,000

Step-by-step explanation:

The formula of simple interest is:

I = P_0rt

Where I is the interest earned after t years

r is the interest rate

P_0 is the initial amount

We know that the investment was $20,000 in two accounts

_______________________________________________

<u><em>For the first account</em></u> r = 0.07 per year.

Then the formula is:

I_1 = P_1r_1t

Where

P_1 is the initial amount in account 1 at a rate r_1 during t = 1 year

I_1 = P_1(0.07)(1)\\\\I_1 = 0.07P_1

<u><em>For the second account </em></u>r = 0.05 per year.

Then the formula is:

I_2 = P_2r_2t

Where

P_2 is the initial amount in account 2 at a rate r_2 during t = 1 year

Then

I_2 = P_2(0.05)(1)\\\\I_2 = 0.05P_2

We know that the final profit was I $1,280.

So

I = I_1 + I_2=1,280

Substituting the values I_1, I_2 and I we have:

1,280 = 0.07P_1 + 0.05P_2

As the total amount that was invested was $20,000 then

P_0 = P_1 + P_2 = 20,000

Then we multiply the second equation by -0.07 and add it to the first equation:

0.07P_1 + 0.05P_2 = 1.280\\.\ \ \ \ \ \ \ \ +\\-0.07P_1 -0.07P_2 = -1400\\-------------

-0.02P_2 = -120\\\\P_2 = 6,000

Then P_1 = 14,000

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