SOLUTION: the difference between the simple interest and compound interest for 3 year at 5% is $61, find the principal.

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Question 227845: the difference between the simple interest and compound interest for 3 year at 5% is $61, find the principal.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
I need both formulas
(1) A%5B1%5D+=+P%2A%281+%2B+t%2Ar%29
and
(2) A%5B2%5D+=+P%2A%281+%2B+r%29%5Et
given:
A%5B2%5D+-+A%5B1%5D+=+61 dollars
r+=+.05
t+=+3
---------------
Subtract (1) from (2)
(2) A%5B2%5D+=+P%2A%281+%2B+r%29%5Et
(1) A%5B1%5D+=+P%2A%281+%2B+t%2Ar%29
A%5B2%5D+-+A%5B1%5D+=+P%2A%28%281+%2B+.05%29%5E3+-+%281+%2B+3%2A.05%29%29
61+=+P%2A%281.05%5E3+-+1.15%29
61+=+P%2A%281.157625+-+1.15%29
61+=+.07625P
P+=+8000
The principle is $8000
check:
(1) A%5B1%5D+=+P%2A%281+%2B+t%2Ar%29
A%5B1%5D+=+8000%2A%281+%2B+.15%29
A%5B1%5D+=+9200
and
(2) A%5B2%5D+=+P%2A%281+%2B+r%29%5Et
(2) A%5B2%5D+=+8000%2A%281.05%29%5E3
A%5B2%5D+=+8000%2A1.157625
A%5B2%5D+=+9261
A%5B2%5D+-+A%5B1%5D+=+9261+-+9200
A%5B2%5D+-+A%5B1%5D+=+61
OK