Morgan has $50,000 to invest and wants to receive $5,000 interest the first year. He puts part in CDs earning 5.75% APY, part in bonds earning 8.7% APY, and the rest in a growth fund earning 14.6% APY. How much should he invest at each rate if he puts the least amount possible in the growth fund?
I can't figure out the work, but the answers are in the back.
They are: $0 CDs, $38,983.05 bonds, and $11,016.95 growth fund.
2007-05-10 10:21:02 · 2 answers · asked by salmonella_jr 3 in Science & Mathematics ➔ Mathematics
He wants a 10% return, so clearly the CDs are not as good as the bonds, so they should be zero. The more he puts in the CDs, the more growth fund will be needed.
Let x = the growth fund investment. Then 50000-x = the bond investment. We want
0.146x + 0.087(50000 - x) = 5000
0.059x + 4350 = 5000
0.059x = 650
x = 11,016.95 = growth fund investment
50000 - x = 38,983.05 = bond investment
0 = CD investment
2007-05-10 10:34:48 · answer #1 · answered by airtime 3 · 0⤊ 0⤋
In order to keep the amount invested in the growth fund to a minimum, nothing can be invested in CDs, as they have the lowest return.
Thus you have
g + b = 50,000
0.146g + 0.087b = 5,000
0.087g + 0.087b = 4,350
0.059g = 650
g = $11,016.95
b = $38,983.05
2007-05-10 17:51:47 · answer #2 · answered by Helmut 7 · 0⤊ 0⤋