SOLUTION: How should a $45,000 investment be split so that the total annual earnings are $1,980, if one portion is invested at 3 percent annual interest amd the rest at 6.5 percent annual in

Algebra ->  Finance -> SOLUTION: How should a $45,000 investment be split so that the total annual earnings are $1,980, if one portion is invested at 3 percent annual interest amd the rest at 6.5 percent annual in      Log On


   

Question 1080259: How should a $45,000 investment be split so that the total annual earnings are $1,980, if one portion is invested at 3 percent annual interest amd the rest at 6.5 percent annual interest?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+I+=+P%2Ar%2At+ ( simple interest )
Let +a+ = amount invested @ 3%
+45000+-+a+ = amount invested @ 6.5%
Let +b+ = earnings from the 3% investment
+1980+-+b+ = earnings from the 6.5% investment
+t+=+1+ yr
------------------------------------------------
(1) +b+=+a%2A.03%2A1+
(2) +1980+-+b+=+%28+45000+-+a+%29%2A.065%2A1+
-------------------------------------------
(1) +b+=+.03a+
and
(2) +1980+-+b+=+2925+-+.065a+
(2) +b+=+.065a+-+945+
Plug (1) into (2)
(2) +.03a+=+.065a+-+945+
(2) +.035a+=+945+
(2) +a+=+27000+
and
+45000+-+a+=+45000+-+27000+
+45000+-+a+=+18000+
---------------------------------
$27,000 @ 3%
$18,000 @ 6.5%
------------------
check:
(1) +b+=+a%2A.03%2A1+
(1) +b+=+27000%2A.03%2A1+
(1) +b+=+810+
and
(2) +1980+-+b+=+%28+45000+-+a+%29%2A.065%2A1+
(2) +1980+-+b+=+18000%2A.065%2A1+
(2) +1980+-+b+=+1170+
(2) +b+=+810+
OK