SOLUTION: An actor invested some money at 6​% simple​ interest, and ​$50,000 more than four times the amount at 7%. The total annual interest earned from the investment was ​$51,440.

Algebra ->  Customizable Word Problem Solvers  -> Finance -> SOLUTION: An actor invested some money at 6​% simple​ interest, and ​$50,000 more than four times the amount at 7%. The total annual interest earned from the investment was ​$51,440.      Log On

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Question 1154298: An actor invested some money at 6​% simple​ interest, and ​$50,000 more than four times the amount at 7%. The total annual interest earned from the investment was ​$51,440. How much did he invest at each​ amount?
Found 3 solutions by josgarithmetic, josmiceli, MathTherapy:
Answer by josgarithmetic(39625) About Me  (Show Source):
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Depends how much time invested

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Use +I+=+P%2Ar%2At+
(1) +I%5B1%5D+=+P%5B1%5D%2Ar%5B1%5D%2At+
(2) +I%5B2%5D+=+P%5B2%5D%2Ar%5B2%5D%2At+
+t+=+1+ ( 1 year investment )
---------------------------
+P%5B2%5D+=+4%2AP%5B1%5D+%2B+50000+
+r%5B1%5D+=+.06+
+r%5B2%5D+=+.07+
+I%5B1%5D+%2B+I%5B2%5D+=+51440+
---------------------------------
+I%5B2%5D+=+51440+-+I%5B1%5D+
---------------------------------
(1) +I%5B1%5D+=+P%5B1%5D%2A.06%2A1+
(2) +51440+-+I%5B1%5D+=+%28+4%2AP%5B1%5D+%2B+50000+%29%2A.07%2A1+
-----------------------------------------------------
(2) +51440+-+I%5B1%5D+=+.28%2AP%5B1%5D+%2B+3500+
(2) +47940+-+I%5B1%5D+=+.28P%5B1%5D+
(2) +I%5B1%5D+=+47940+-+.28P%5B1%5D+
---------------------------------------------
(1) +I%5B1%5D+=+.06P%5B1%5D+
(1) ++47940+-+.28P%5B1%5D+=+.06P%5B1%5D+
(1) +.34P%5B1%5D+=+47940+
(1) +P%5B1%5D+=+141000+
and
(1) +I%5B1%5D+=+.06%2A141000+
(1) +I%5B1%5D+=+8460+
and
+I%5B2%5D+=+51440+-+I%5B1%5D+
+I%5B2%5D+=+51440+-+8460+
+I%5B2%5D+=+42980+
-----------------------
+P%5B2%5D+=+4%2AP%5B1%5D+%2B+50000+
+P%5B2%5D+=+4%2A141000+%2B+50000+
+P%5B2%5D+=+564000+%2B+50000+
+P%5B2%5D+=+614000+
-------------------------------
$141,000 @ 6%
$614,000 @ 7%
--------------------
check:
(2) +51440+-+I%5B1%5D+=+%28+4%2AP%5B1%5D+%2B+50000+%29%2A.07%2A1+
(2) +51440+-+8460+=+%28+4%2A141000+%2B+50000+%29%2A.07%2A1+
(2) +42980+=+%28+564000+%2B+50000+%29%2A.07+
(2) +42980+=+614000%2A.07+
(2) +42980+=+42980+
OK




Answer by MathTherapy(10555) About Me  (Show Source):
You can put this solution on YOUR website!
An actor invested some money at 6​% simple​ interest, and ​$50,000 more than four times the amount at 7%. The total annual interest earned from the investment was ​$51,440. How much did he invest at each​ amount?
Let amount invested in 6% fund, be S
Then amount invested in the 7% fund = 4S + 50,000
We then get the following INTEREST equation: .06S + .07(4S + 50,000) = 51,440
.06S + .28S + 3,500 = 51,440
.34S = 47,940
S, or amount invested in the 6% fund =
Amount invested in the 7% fund =
It's as SIMPLE as that!!