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4. A perpetuity paying $100 on the last day of each year was purchased on January 1, 2000. On Jan...

4. A perpetuity paying $100 on the last day of each year was purchased on January 1, 2000. On January 1, 2005, the perpetuity was exchanged for a 15-year annuity-due with semiannual payments of amount X. Find X if the interest rate is 6% convertible monthly. (Answer: $80.67)

Math Interest Theory / Financial Math
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Answer #1

rate convertible annually=((1+6%/12)^(12/1)-1)*1=6.17%

rate convertible semi-annually=((1+6%/12)^(12/2)-1)*2=6.08%

X/(6.08%/2)*(1-1/(1+6.08%/2)^(2*15))*(1+6.08%/2)=100/6.17%

=>X=100/6.17%*(6.08%/2)/(1-1/(1+6.08%/2)^(2*15))*1/(1+6.08%/2)

=>X=80.66513539

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