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#1




SOA Sample Question #85 and #101
SOA Sample #85
The present value of a perpetuity paying 1 every two years with first payment due immediately is 7.21 at an annual effective rate of i. Another perpetuity paying R every three years with the first payment due at the beginning of year two has the same present value at an annual effective rate of i + 0.01. Calculate R. The answer is 1.74. This is how SOA does it: I got i = 0.077511 and j = (1 + i)^3  1 = 0.2861788. I used the following equation in order to find R, (v^2)(adotinfinity)(R) = 7.21 With v = 1/1+j = 0.7774969 and I got R = 2.65384, which is definitely incorrect. I can't understand where I am going wrong the SOA's solution is not helpful either. Any help is appreciated! Thank you! SOA Sample #101 A 30year annuity is arranged to pay off a loan taken out today at a 5% annual effective interest rate. The first payment of the annuity is due in ten years in the amount of 1,000. The subsequent payments increase by 500 each year. Calculate the amount of the loan. The answer is 64,257. This is how SOA does it: My only concern is why are there 30 payments? Shouldn't there by only 20 payments considering the first payment is due in 10 years (i.e., deferred annuity)? Thank you for your help! 
#2




30year annuity means the annuity lasts for 30 years. In this case, from the 10th to the 40th year.
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#3




For the first one, the beginning of year 2 is time 1 and the v should be at the one year rate.

#4




Oh, so it's not a deferred annuity? It's just an ordinary 30  year annuity?

#5




Got it! Thank you so much for your help!

Tags 
annuity, financial mathematics, interest rate, perpetuity 
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