A-6 Appendix A Solutions to Self-Test Questions and Problems
g. E" ective annual rate! (^)! 1 # I NOM^
M
(^) "
M
" 1.0
! (^)! 1 # 0.08 2 "
2
" 1! (1.04)^2 " 1
! 1.0816 " 1! 0.0816! 8.16%
APR! IPER $ M
! 0.04 $ 2! 0.08! 8%
Bank A’s effective annual rate is 8.24%:
E" ective annual rate! (^)! 1 # 0.08 4 "
4
" 1.0
! (1.02)^4 " 1
! 1.0824 " 1
! 0.0824! 8.24%
Now Bank B must have the same effective annual rate:
(^)! 1 # I NOM^
12
(^) "
12
"1.0! 0.0824
(^)! 1 #
I NOM
12 "
12
! 1.0824
1 #
I NOM
12! (1.0824)1/12
1 #
I NOM
12! 1.00662
I NOM
12! 0.00662
INOM! 0.07944! 7.94%
Thus, the two banks have different quoted rates—Bank A’s quoted rate is 8%,
while Bank B’s quoted rate is 7.94%; however, both banks have the same effec-
tive annual rate of 8.24%. The difference in their quoted rates is due to the dif-
ference in compounding frequency.
Chapter 6
a. Average in# ation over 4 years! (2% # 2% # 2% # 4%)/4! 2.5%
b. T 4! rRF # MRP 4
! r # IP 4 # MRP 4
! 3% # 2.5% # (0.1)3%
! 5.8%
c. C4, BBB! r # IP 4 # MRP 4 # DRP # LP
! 3% # 2.5% # 0.3% # 1.3% # 0.5%
! 7.6%
d. T 8! r # IP 8 # MRP 8
! 3% # (3 $ 2% # 5 $ 4%)/8 # 0.7%
! 3% # 3.25% # 0.7%
! 6.95%
e. C8, BBB! r # IP 8 # MRP 8 # DRP # LP
! 3% # 3.25% # 0.7% # 1.3% # 0.5%
! 8.75%