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Suppose a deposit of $ 2 , 000 in a savings account that paid an annual interest rate r (compounded yearly) is worth $ 2 , 209 after 2 years. using the formula a = p ( 1 + r ) t , we have 2 , 209 = 2 , 000 ( 1 + r ) 2 solve for r to find the annual interest rate (to the nearest tenth).

User Komar
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1 Answer

10 votes

Answer:

5.1% (nearest tenth)

Explanation:

Annual Compound Interest Formula


\large \text{$ \sf A=P\left(1+r\right)^(t) $}

where:

  • A = final amount
  • P = principal amount
  • r = interest rate (in decimal form)
  • t = time (in years)

Given:

  • A = $2,209
  • P = $2,000
  • t = 2 years

Substitute the given values into the formula and solve for r:


\implies \sf 2209=2000\left(1+r\right)^(2)


\implies \sf (2209)/(2000)=(1+r)^2


\implies \sf 1.1045=(1+r)^2


\implies \sf √(1.1045)=1+r


\implies \sf r = √(1.1045)-1


\implies \sf r = 0.05095194942...


\implies \sf r = 5.095194942...\%

Therefore, the annual interest rate is 5.1% (nearest tenth)

User HChen
by
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