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On January 1, 2011, Maria invested $1,000 at 6 percent interest per year for three years (with yearly capitalization). The CPI stood at 100 in January 1, 2011. At year later it climbed to 105 and on January 1, 2013 was 110, and on January 1, 2014, the day Marias investment matured, the CPI was at 118. Find the real interest rate that Maria's total real return over the 3-year period.

Sagot :

Based on the information given, the real interest rate that Maria's total real return over the 3-year period will be 0.94%.

Inflation rate in 2012 will be:

= (105/100) - 1 = 5%

Inflation rate in 2013 will be:

= (110/105) - 1 = 4.76%

Inflation rate in 2014 will be:

= (118/100) - 1 = 7.27%

The average inflation rate for three years will be 5.67%.

The real return for 2012 will be:

= (1 + 0.06)  / (1 + 0.05) - 1

= 0.95%

The real return for 2013 will be:

= (1 + 0.06) / (1 + 0.0476) - 1

= 1.18%

The real return for 2014 will be:

= (1 + 0.06) / (1 + 0.0727) - 1

= -1.18%

Therefore, the rate of return over the three years period will be:

= (1 + 0.095) × (1 + 0.118) × (1 - 0.118) - 1

= 0.94%

In conclusion, the correct option is 0.94%.

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