Below are six different mortgage options that are available to you the borrower.
ID: 2742537 • Letter: B
Question
Below are six different mortgage options that are available to you the borrower. You would like to determine what the rates might be if you were to wait to finance your property. Based on the information given answer the questions that follow:
5 year rate = 3.0%
10 year rate = 3.5%
15 year rate = 4.0%
20 year rate = 4.125%
30 year rate = 4.25%
40 year rate = 4.5%
A)What is the five year mortgage rate ten years from now?
B)What is the ten year mortgage rate ten years from now?
C)What is the ten year mortgage rate twenty years from now?
D)What is the fifteen year mortgage rate fifteen years from now?
Explanation / Answer
Part A
Five year rate 10 years from now = ((1+r15)^15/ (1+r10)^10)^(1/5) -1
= ((1+0.04)^15 / (1+0.035)^10))^0.20 -1
= (1.276723)^0.20 -1
= 5.01%
Part B
10 year rate 10 years from now = ((1+r20)^20/ (1+r10)^10)^(1/10) -1
= ((1+0.04125)^20 / (1+0.035)^10))^0.10 -1
= (1.591097)^0.10 -1
= 4.75%
Part C
10 year rate 20 years from now = ((1+r30)^30/ (1+r20)^20)^(1/10) -1
= ((1+0.0425)^30 / (1+0.04125)^20))^0.10 -1
= (1.5530)^0.10 -1
= 4.50%
Part D
15 year rate 10 years from now = ((1+r30)^30/ (1+r15)^15)^(1/15) -1
= ((1+0.0425)^30 / (1+0.04)^10))^(1/15) -1
= (1.935449)^(1/15) -1
= 4.50%
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