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P=500(1.035)^(n)
The value, 
P, in dollars, of 
$500 invested in an account earning interest at a constant rate, compounded annually, after 
n years is given by the equation shown, assuming no additional investments or withdrawals are made. What is the annual interest rate on the account, in percent?
(Ignore the 
% symbol when entering your answer. For example, if the answer is 
11.2%, enter 11.2 .)

P=500(1.035)n P=500(1.035)^{n} \newlineThe value, P P , in dollars, of $500 \$ 500 invested in an account earning interest at a constant rate, compounded annually, after n n years is given by the equation shown, assuming no additional investments or withdrawals are made. What is the annual interest rate on the account, in percent?\newline(Ignore the % \% symbol when entering your answer. For example, if the answer is 11.2% 11.2 \% , enter 1111.22 .)

Full solution

Q. P=500(1.035)n P=500(1.035)^{n} \newlineThe value, P P , in dollars, of $500 \$ 500 invested in an account earning interest at a constant rate, compounded annually, after n n years is given by the equation shown, assuming no additional investments or withdrawals are made. What is the annual interest rate on the account, in percent?\newline(Ignore the % \% symbol when entering your answer. For example, if the answer is 11.2% 11.2 \% , enter 1111.22 .)
  1. Given formula analysis: We are given the formula for compound interest: P=500(1.035)nP = 500(1.035)^{n}. To find the annual interest rate, we need to look at the base of the exponent, which is 1.0351.035 in this case. This base represents the growth factor for one year, which includes the original amount plus the interest rate. To find the interest rate, we subtract 11 from the growth factor.
  2. Calculate interest rate: Calculate the interest rate by subtracting 11 from the growth factor:\newlineInterest rate = 1.03511.035 - 1\newlineInterest rate = 0.0350.035
  3. Convert to percent: Convert the interest rate from decimal form to percent form by multiplying by 100100:Interest rate in percent=0.035×100\text{Interest rate in percent} = 0.035 \times 100Interest rate in percent=3.5%\text{Interest rate in percent} = 3.5\%

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