Krzys’ Ostaszewski, http://www.math.ilstu.edu/krzysio/, Exercise 75, 10/21/6
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Course 140 Practice Examination 140-82-96, Problem No. 1
Jennifer deposits 1000 into a bank account. The bank credits interest at a nominal annual
rate of i convertible semi-annually for the first 7 years and a nominal annual rate of 2i
convertible quarterly for all years thereafter. The accumulated amount in the account at
the end of 5 years is X. The accumulated amount in the account at the end of 10.5 years is
1980. Calculate X.
A. 1200
B. 1225
C. 1250
D. 1275
E. 1300
Solution.
Using a nominal annual rate of i convertible semi-annually for the first 7 years and a
nominal annual rate of 2i convertible quarterly for all years thereafter we obtain
2!7
4!3.5
i%
2i %
"
"
1000 ! $ 1 + ' ! $ 1 + '
= 1980.
#
#
2&
4&
This implies
28
i$
!
#" 1 + &% = 1.98,
2
and
1
#
&
i = 2 ! % 1.98 28 " 1( ) 4.939268%.
$
'
Finally
i%
"
X = 1000 ! $ 1 + '
#
2&
Answer D.
10
( 1276.30.
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