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Financial Mathematics Old FM Forum

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  #1  
Old 02-23-2019, 08:09 PM
Mitsu96 Mitsu96 is offline
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Default SOA Sample Question #163 and #169

SOA Sample #163

John took out a 20-year loan of 85,000 on July 1, 2005 at an annual nominal interest rate of 6% compounded monthly. The loan was to be paid by level monthly payments at the end of each month with the first payment on July 31, 2005.
Right after the regular monthly payment on June 30, 2009, John refinanced the loan at a new annual nominal rate of 5.40% compounded monthly, and the remaining balance will be paid with monthly payments beginning July 31, 2009. The amount of each payment is 500 except for a final drop payment.
Calculate the date of John’s last payment.

The answer is May 31, 2030.

This is how SOA does it:

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And I understand this way of solving the question. However, I tried to find the accumulated value at 48 months and used that to get the number of months until the final payment, n. So, this is what I did:

AV48 = 608.9664(s-angle-48) = 32,943.762. Thus,
32,943.762 = 500(-angle-n).
I got n = 78.32, which is miserably wrong. I don't understand what logic/concept am I missing out if I use the accumulated value to find the last payment date.

Any help is appreciated! Thank you!

SOA Sample #169

Claire purchases an eight-year callable bond with a 10% annual coupon rate payable semiannually. The bond has a face value of 3000 and a redemption value of 2800.
The purchase price assumes the bond is called at the end of the fourth year for 2900, and provides an annual effective yield of 10.0%.
Immediately after the first coupon payment is received, the bond is called for 2960. Claire’s annual effective yield rate is i.
Calculate i.

The answer is 0.10759.

This is how SOA does it:

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I got the bond price after the fourth year as 2955.08. However, I don't understand how we can use that to get the annual effective yield rate (i.e., the highlighted part) and I don't know how else to proceed with the problem.

Any help is appreciated! Thank you!
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Old 02-23-2019, 09:07 PM
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Breadmaker Breadmaker is offline
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#163: Restrospective accumulation requires you to roll up the original loan balance, then deduct the accumulated value of the payments to get the outstanding principal

#169: j is nominal semi-annual/2. (1+j)^2 = 1+effective annual. I'll leave the algebra to you. $2,955.08 is what Claire paid at time 0 for this bond, not after 4 years.
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Old 02-24-2019, 05:40 PM
Mitsu96 Mitsu96 is offline
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Quote:
Originally Posted by Breadmaker View Post
#163: Restrospective accumulation requires you to roll up the original loan balance, then deduct the accumulated value of the payments to get the outstanding principal

#169: j is nominal semi-annual/2. (1+j)^2 = 1+effective annual. I'll leave the algebra to you. $2,955.08 is what Claire paid at time 0 for this bond, not after 4 years.

Wow! Your replies make so much sense! Thank you!
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