SOLUTION: Please help me understand this The formula when interest is compounded n time per year is A=p(1+r/n)nt Where A is the accrued amount after t years, P is the starting principa

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Question 1093899: Please help me understand this
The formula when interest is compounded n time per year is A=p(1+r/n)nt
Where A is the accrued amount after t years, P is the starting principal, and r is the interest rate, expressed as a decimal, that is compounded n times a year. If you invest $1000 at an interest rate of 7%, and leave it there for 30 years, determine your ending balance if the interest is compounded.
1. Once a year 2. Twice a year

Found 2 solutions by stanbon, josmiceli:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
The formula when interest is compounded n time per year is A=p(1+r/n)nt
Where A is the accrued amount after t years, P is the starting principal, and r is the interest rate, expressed as a decimal, that is compounded n times a year. If you invest $1000 at an interest rate of 7%, and leave it there for 30 years, determine your ending balance if the interest is compounded.
1. Once a year
A(t) = P(1+(r/n))^(nt)
Let t = 1
A(30) = 1000(1+(0.07/1))^(1*30)
A(1) = 1000(1.07)^30
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2. Twice a year
A(30) = 1000(1+(0.07/2))^(2*30)
A(30) = 1000(1.035)^60
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Cheers,
Stan H.
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Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+A+ is the amount you end up with after +t+ years
+P+ is the amount you begin investing with
+r+ is the interest rate
+n+ is the number of times you compound per year
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Note that unless you know what +n+ and +t+ are
for instance, if +nt+=+6+, you could have +1%2A6+=+6+ or
+2%2A3+=+6+.
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(1) +n+=+1+
+A+=+P%2A%28+1+%2B+r%2Fn+%29%5E%28nt%29+
+A+=+1000%2A%28+1+%2B+.07%2F1+%29%5E%28+1%2A30+%29+
+A+=+1000%2A1.07%5E30+
+A+=+1000%2A7.6123+
+A+=+7612.3+
$7,612.30 ending balance
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(2) +n+=+2+
+A+=+P%2A%28+1+%2B+r%2Fn+%29%5E%28nt%29+
+A+=+1000%2A%28+1+%2B+.07%2F2+%29%5E%282%2A30%29+
+A+=+1000%2A1.035%5E60+
+A+=+1000%2A7.8781+
+A+=+7878.1+
$7,878.10 ending balance
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