Tom won 100,000 dollars in the lottery. he invested part of the money in real estate with an annual return of 5%, and another part in a money market account at 4.5% interest. He invested the rest, which amounted to $20,000 less than the sum of the other 2 parts, in certificates of deposit that pay 3.75%. If the annual interest on the money was $4450, how much was invested at each rate?
2007-09-13 12:33:03 · 4 answers · asked by Adam M 2 in Science & Mathematics ➔ Mathematics
50000 at 5%
10000 at 4.5%
40000 at 3.75%
its a little confusing but...
to start, the 3rd amount is 20000 less than the sum of the other 2 so:
100000 = x+y+z
z = x+y-20000
z = 100000-x-y
100000-x-y = x+y-20000
120000 = 2x+2y
60000 = x+y
therefor z = 40000
next, the interest on the 40000 at 3.75% is $1500 (40000*.0375)
so the total interest left unaccounted for is 4450-1500=2950
so $2950 = .05x + .045y
we know x+y = 60000 so solve for x
x = 60000 - y
substitute 2950 = .05(60000 - y) + .045y
2950 = 3000 - .05y +.045y
-50 = -.0005y
y = 10000
so x = 50000 since x+y=60000
get it? =)
2007-09-13 12:46:59 · answer #1 · answered by joem 2 · 0⤊ 0⤋
x = amount invested in real estate at 5%
y = amount invested in MM at 4.5%
x+y-20000 = amount invested in CDs at 3.75%
So 2x+2y -20000 = 100000
x + y = 60000 <-- Eq 1
.05x+ .045y+.0375(x+y-20000) = 4450
.0875x + .0825y - 750 = 4450
.0875x + .0825y = 5200 <-- Eq 2
Now Solve Eq 1 and Eq 2 simultaneously and you'll have your answer.
2007-09-13 19:58:14 · answer #2 · answered by ironduke8159 7 · 0⤊ 0⤋
I suggest that joem show how he reached these answers...
2007-09-13 19:48:30 · answer #3 · answered by GeriGeri 5 · 0⤊ 0⤋
sry im doing this stuff as well but not as complicated.. i've been trying to answer it but cant.. sry
2007-09-13 19:41:11 · answer #4 · answered by Anonymous · 0⤊ 0⤋