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To calculate this, break up the interest into four pieces and put them to the power of n. That is

  • Annual interest = P(1+i)4n
  • Quarterly = P(1+i/4)n
  • i/4 = 0.07/4, so
  • (1.0175)4 ~ 1.072, which is the rate of change per annum. The effective i is
  • 100%*(1.072-1)/1 = 7.2%
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Q: What is the effective annual interest rate r of 7 percent compounded quarterly?
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