SOLUTION: Use the compound interest formula Upper A= P( 1 + r )^t to find the annual interest​ rate, r, if in 2 years an investment of $2,000 grows to $ 3,380. The rate is ? %

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Question 1128472: Use the compound interest formula Upper A= P( 1 + r )^t to find the annual interest​ rate, r, if in 2 years an investment of $2,000 grows to $ 3,380.
The rate is ? %
Found 2 solutions by MathLover1, MathTherapy:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

+A=+P%28+1+%2B+r+%29%5Et
t=2 years
P=2000 grows to
A=3380
r=?

+3380=+2000%28+1+%2B+r+%29%5E2
+3380%2F2000=%28+1+%2B+r+%29%5E2
+1.69=1+%2B+2r+%2Br%5E2
+r%5E2%2B+2r+%2B1-1.69=0

+r%5E2%2B+2r-0.69=0
+100r%5E2%2B+200r-69=0

r+=+%28-200+%2B-+sqrt%28+200%5E2-4%2A100%2A%28-69%29+%29%29%2F%282%2A100%29+
r+=+%28-200+%2B-+sqrt%28+40000%2B27600+%29%29%2F200+

r+=+%28-200+%2B-+sqrt%28+67600+%29%29%2F200+

r+=+%28-200+%2B-+260%29%2F200+
r+=+%28-10+%2B-+13%29%2F10+ ...need only positive solution

r+=+%28-10+%2B+13%29%2F10+

r+=+3%2F10

r=0.3 => r=30%



Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
Use the compound interest formula Upper A= P( 1 + r )^t to find the annual interest​ rate, r, if in 2 years an investment of $2,000 grows to $ 3,380.
The rate is ? %
matrix%281%2C3%2C+A%2C+%22=%22%2C+P%281+%2B+r%29%5E2%29

matrix%281%2C3%2C+%223%2C380%22%2C+%22=%22%2C+%222%2C000%22%281+%2B+r%29%5E2%29 ------- Substituting 3,800 for A, $2,000 for P, and 2 for t

matrix%281%2C3%2C+%223%2C380%22%2F%222%2C000%22%2C+%22=%22%2C+%281+%2B+r%29%5E2%29

matrix%281%2C3%2C+169%2F100%2C+%22=%22%2C+%281+%2B+r%29%5E2%29          OR     matrix%281%2C3%2C+1.69%2C+%22=%22%2C+%281+%2B+r%29%5E2%29 

     OR    matrix%281%2C3%2C+%22%22%2B-+sqrt%281.69%29%2C+%22=%22%2C+sqrt%28%281+%2B+r%29%5E2%29%29 

matrix%281%2C3%2C+13%2F10%2C+%22=%22%2C+1+%2B+r%29              OR    matrix%281%2C3%2C+1.3%2C+%22=%22%2C+1+%2B+r%29 ------- ONLY solution > 0 is applicable HERE

Annual interest rate, or  

That's all!! Nothing more, nothing less!