week 13 8. Compute the effective annual rates of the following: a. $1 million ma
ID: 2665933 • Letter: W
Question
week 13
8. Compute the effective annual rates of the following:
a. $1 million maturing in 90 days with a stated annual rate of 6
percent. Fees are 0.02 percent of the principal.
b. $15 million maturing in 60 days with a stated annual rate of 7.6 percent. Fees are 0.05 percent of the principal.
c. $500,000 maturing in 180 days with a stated annual rate of 8.25 percent. Fees are 0.03 percent of the principal.
d. $50 million maturing in 210 days with a stated annual rate of6.5 percent. Fees are 0.10 percent of the principal
Explanation / Answer
Computing the effective annual rates of the following:
(a) $1 million maturing in 90 days with a stated annual rate of 6 percent. Fees are 0.02 percent of the principal.
90 days = Quarter
EAR = (1+APR / 4)4 – 1
EAR = (1+0.06 / 4)4 – 1
EAR = (1.015)4 – 1
EAR = 1.06136355 – 1
EAR = 0.06136355 (or) 6.136%
EAR = 6.136%
(b) $15 million maturing in 60 days with a stated annual rate of 7.6 percent. Fees are 0.05 percent of the principal.
Maturity period = 60 days
60 days / 360 =
EAR = (1+APR / 4)4 – 1
EAR = (1+0.076 / 0.16666)0.16666 – 1
EAR = (1.4560182)0.16666 – 1
EAR = 1.064616958 – 1
EAR = 0.064616958 (or) 6.46%
EAR = 6.46%
(c) $500,000 maturing in 180 days with a stated annual rate of 8.25 percent. Fees are 0.03 percent of the principal.
Maturity period = 180 days
180 days / 360 = 0.5
EAR = (1+APR / 4)4 – 1
EAR = (1+0.0825 / 2)2 – 1
EAR = (1.04125)2 – 1
EAR = 1.084201563 – 1
EAR = 0.084201563 (or) 8.42%
EAR = 8.42%
(d) $50 million maturing in 210 days with a stated annual rate of 6.5 percent. Fees are 0.10 percent of the principal.
Maturity period = 210 days
210 days / 360 = 0.58333
EAR = (1+APR / 4)4 – 1
EAR = (1+0.065 / 0.58333)0.58333 – 1
EAR = (1.111429)0.58333 – 1
EAR = 1.063565 – 1
EAR = 0.063565 (or) 6.3565%
EAR = 6.3565%
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