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Andrews [41]
3 years ago
7

You have $4000 to invest. If you'd like to earn exactly $638

Mathematics
1 answer:
Natali [406]3 years ago
5 0

Answer:

8%: $1554

21%: $2446

Step-by-step explanation:

This is a simple interest problem.

The simple interest formula is given by:

E = P*I*t

In which E are the earnings, P is the principal(the initial amount of money), I is the interest rate(yearly, as a decimal) and t is the time.

After t years, the total amount of money is:

T = E + P.

In this question:

Two earnings, that i am going to call A(8% per year) and B(21% per year).

Two principals, for A i am going to call P and for B it is the rest, so 4000 - P.

A:

One year, so t = 1

8% interest, so r = 0.08

Earnings A.

A = P*I*t

A = 0.08P

B:

21% interest, so r = 0.21

Principal (4000 - P).

B = P*I*t

B = 0.21*(4000 - P)

You'd like to earn exactly $638 in interest each year.

This means that A + B = 638

Then

B = 638 - A

Now we have to solve the following system:

A = 0.08P

638 - A = 0.21*(4000 - P)

So, on the second equation:

A = 638 - 0.21*(4000 - P)

Replacing on the first:

A = 0.08P

638 - 0.21*(4000 - P) = 0.08P

638 - 840 + 0.21P = 0.08P

0.21P - 0.08P = 840 - 638

0.13P = 202

P = \frac{202}{0.13}

P = 1553.8

Rounding up to the nearest integer

P = 1554.

So on A, the 8% interest, you invest $1554.

On B, the 21% interest, you invest 4000 - 1554 = $2446.

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