Hans invests $550 at a rate of x% per year compound interest.
At the end of 10 years he has a total amount of $638.30, correct to the nearest cent.
Find the rate value
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Answer:
A = p(1 + r/n)nt
A= final value = $638.30
p= principal = $550
r = interest rate = x/100
n= number times compounded per year=1
t = time in years = 10
638.3 = 550(1 + x/100)10
638.3/550 = (1 + x/100)10
Take the 10th root of both sides
10√(638.3/550) = 1 + x/100
A scientific calculator using y√x gives:
1.015 = 1 + x/100
subtract 1 from both sides
0.015 = x/100
multiply both sides by 100
x = 1.5
The annual percentage rate is 1.5%
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Check:
550(1 + 1.5/100)10 = 550(1.015)10 = $638.30
Answer matches and is correct.
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