2. A bond pays a 5% quarterly on a 30/360 basis.
(a) What yield on an actual/360 basis is equivalent to the 5% yield on a 30/360 basis when the coupon period is 89 days?
(b) What is the mortgage equivalent yield of a quarterly paying bond with a 5% yield?
can someone explain this in detail please, I am really confused on how to calculate interest using different day counts
Answer (a):
Quarterly payment on a 30/360 basis is payment for 90 days.
Actual coupon period is 89 days
The yield on an actual/360 basis which is equivalent to the 5% yield on a 30/360 basis = 90 /89 * 5% = 5.0562%
The yield on an actual/360 basis which is equivalent to the 5% yield on a 30/360 basis = 5.0562%
Answer (b):
Effective annual rate of quarterly paying bond with a 5% yield = (1 + 5% / 4) 4 - 1=5.09453%
Let us assume mortgage equivalent yield = r
Effective annual rate of mortgage with r yield = (1 + r / 12) 12- 1
Hence:
=> (1 + r / 12) 12- 1 = 5.09453%
=> (1 + r / 12) 12 = 5.09453% + 1
=> 1 + r / 12 = (1.0509453) 1/12 = 1.004149
> r / 12 = 1.004149 - 1 = 0.004149
=> r = 0.004149 * 12 = 4.98%
Mortgage equivalent yield = 4.98%
2. A bond pays a 5% quarterly on a 30/360 basis. (a) What yield on an...
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