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
