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Devon invested $10,500 in three different mutual funds. A fund containing large cap stocks made a 6.7% return in 1 yr. A real estate fund lost 15.6% in 1 yr, and a bond fund made 4.9% in 1 yr. The amount invested in the large cap stock fund was four times the amount invested in the real estate fund. If Devon had a net return of $315 across all investments, how much did he invest in each fund

Respuesta :

Answer:

Amount invested in a fund containing large cap stocks = $6,000

Amount invested in a real estate fund = $1,500

Amount invested in a bond fund = $3,000

Explanation:

Let:

x = Amount invested in a fund containing large cap stocks = 4 * y = 4y

y = Amount invested in a real estate fund

z = Amount invested in a bond fund =

For total amount invested, we have:

T = total amount invested = x + y + z = $10,500

Therefore, we have:

4y + y + z = $10,500

5y + z = $10,500 ……………………….. (1)

From equation (1), we have:

z = 10,500 - 5y …………………….(2)

Also, for the net returns, we have:

6.7%x - 15.6%y + 4.9%z = $315

0.067(4y) - 0.156y + 0.049z = 315

0.268y - 0.156y + 0.049z = 315

0.112y + 0.049z = 315 ………………… (3)

Substitute equation (2) for z in equation (3), we have:

0.112y + 0.049(10,500 - 5y) = 315

0.112y + 514.50 - 0.245y = 315

0.112y - 0.245y = 315 - 514.50

-0.133y = -199.50

y = -199.5 / -0.133

y = 1,500

x = 4y = 4 * 1,500 = 6,000

From equation (2), we have:

z = 10,500 - 5y = 10,500 - (5 * 1,500) = 3,000

Therefore, we have:

Amount invested in a fund containing large cap stocks = $6,000

Amount invested in a real estate fund = $1,500

Amount invested in a bond fund = $3,000

Checking this, we have:

Total amount invested = $6,000 + $1,500 + $3,000 = $10,500

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