Question

You invested $ 100 on January 1 , 2007 . The investment was worth $ 190 on July 1 , 2012 . The effective rate of return for the first year was 12 % . Determine the annual effective rate of return from January 1 , 2008 , to July 1 , 2012

Answer 1

On January 1, 2008 our investment is worth 100 * (1 + 0.12) = $112

The number of 6-month periods between January 1 , 2008 and July 1 , 2012 is 9.

n = 9

FV = $190

PV = $112

r = ?

FV = PV * (1 + r)^n

(1 + r)^n = FV/PV

(1 + r) = (FV/PV)^(1/n)

1 + r = (FV/PV)^(1/n) - 1

r = (FV/PV)^(1/n) - 1

r = (190/112)^(1/9) - 1

r = 0.06048359132

This r is the effective 6-month rate

The annual effective rate = (1 + 0.06048359132)^2 - 1

The annual effective rate = 0.1246254475

The annual effective rate = 12.46254475%

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