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ASM pg. 180 #1 help
ASM 12th ed. pg. 180 #1
A loan of 10,000 is to be amortized in 10 annual payments beginning 6 months after the date of the loan. The first payment, X, is half as large as the other payments. Interest is calculated at an annual effective rate of 5% for the first 4.5 years and 3% thereafter. Determine X. I am having a difficult time understanding the book's answer, and I feel like I'll learn more if I can understand why my approach is incorrect. I'm sure I made some kind of newbie mistake here, and I am hoping for enlightenment! If I understand the question correctly, first payment is six months out and then payments proceed one year apart. I just pulled everything back an additional 0.5 year, the first payment X back 0.5 year, the next 4 @ 5% by 1.5 years and the next 5 @ 3% by 5.5 years. All v is at 5%. 10,000 = Xv^.5 + 2Xv^1.5 a45% + 2Xv^5.5 a53% Solving for X, I get 686.31. The correct answer is 656. What am I doing wrong? 
#2




Quote:
2Xv^5.5 a53% again, immediate or due? And is that v^5.5 at 5%? v^5.5 at 5% would not be right 
#3




Hi Gandalf. I intended annuity immediate. But your question got me to realize my equation was unclear.
So I went back and tried to reformulate it from the start. Maybe this one uses better notation for annuities. All annuity immediate and all v is @5% I used the first payment time when X is paid as the comparison date. PV immediately before first payment of X is 10,000(1.05)^ .5 = 10246.95. PV immediately after payment of X is 10,246.95  X PV in terms of remaining payments at comparison date: 2X a4@5 + 2X v^4 a5@3 10,000(1.05)^.5  X = 2X a4@5 + 2X v^4 a5@3. Then, solving X = 655.70. Now I understand the book's version, too. 
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asm 12th, interest rates, present value 
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