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An annuity pays 3 at the end of each year for 14 years
An annuity pays 3 at the end of each year for 14 years. Another annuity pays 4.199 at the end of each year for 7 years. At an annual effective rate of interest i
, the PV of both annuities are equal. Calculate i
Expert Solution
Present value of 14 year annuity due=3* (1- 1/ (1+ i)^ 14)/ (1- 1/ (1+ i))
Present value of 7 year annuity due=4.199* (1- 1/ (1+ i)^ 7)/(1- 1/(1+ i))
=>3* (1- 1/ (1+ i)^ 14)/ (1- 1/ (1+ i)))=4.199* (1- 1/ (1+ i)^ 7)/(1- 1/(1+ i))
=> 3* (1- 1/ (1+ i)^ 14)= 4.199* (1- 1/ (1+ i)^ 7)
=> (1- 1/ (1+ i)^ 7)= 4.199/ 3
=> (1- 1/ (1+ i)^ 7)= 1.3997
=> 1/ (1+ i)^ 7= 0.3997
=> (1+ i)^ 7= 1/ 0.3997
=> (1+ i)^ 7= 2.5019
=> (1+ i)= (2.5019)^ 1/7
=> (1+ i)= 1.1400
=> i= 1.1400- 1
=> i= 0.1400
= 14%
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