In Problems 79-82, assume that the annual interest rate on a credit card is 25.74 % and interest is calculated by the average daily balance method. The unpaid balance at the start of a 28 -day billing cycle was $ 955.13. A $ 5 , 000 purchase was made on the first day of the billing cycle and a $ 50 payment was credited to the account on day 21 . How much interest will be charged at the end of the billing cycle?
In Problems 79-82, assume that the annual interest rate on a credit card is 25.74 % and interest is calculated by the average daily balance method. The unpaid balance at the start of a 28 -day billing cycle was $ 955.13. A $ 5 , 000 purchase was made on the first day of the billing cycle and a $ 50 payment was credited to the account on day 21 . How much interest will be charged at the end of the billing cycle?
Solution Summary: The author calculates the interest that will be charged at the end of the billing cycle by the average daily balance method.
In Problems 79-82, assume that the annual interest rate on a credit card is
25.74
%
and interest is calculated by the average daily balance method.
The unpaid balance at the start of a
28
-day billing cycle was
$
955.13.
A
$
5
,
000
purchase was made on the first day of the billing cycle and a
$
50
payment was credited to the account on day
21
. How much interest will be charged at the end of the billing cycle?
Keity
x२
1. (i)
Identify which of the following subsets of R2 are open and which
are not.
(a)
A = (2,4) x (1, 2),
(b)
B = (2,4) x {1,2},
(c)
C = (2,4) x R.
Provide a sketch and a brief explanation to each of your answers.
[6 Marks]
(ii)
Give an example of a bounded set in R2 which is not open.
[2 Marks]
(iii)
Give an example of an open set in R2 which is not bounded.
[2 Marks
2.
(i)
Which of the following statements are true? Construct coun-
terexamples for those that are false.
(a)
sequence.
Every bounded sequence (x(n)) nEN C RN has a convergent sub-
(b)
(c)
(d)
Every sequence (x(n)) nEN C RN has a convergent subsequence.
Every convergent sequence (x(n)) nEN C RN is bounded.
Every bounded sequence (x(n)) EN CRN converges.
nЄN
(e)
If a sequence (xn)nEN C RN has a convergent subsequence, then
(xn)nEN is convergent.
[10 Marks]
(ii)
Give an example of a sequence (x(n))nEN CR2 which is located on
the parabola x2 = x², contains infinitely many different points and converges
to the limit x = (2,4).
[5 Marks]
2.
(i) What does it mean to say that a sequence (x(n)) nEN CR2
converges to the limit x E R²?
[1 Mark]
(ii) Prove that if a set ECR2 is closed then every convergent
sequence (x(n))nen in E has its limit in E, that is
(x(n)) CE and x() x
x = E.
[5 Marks]
(iii)
which is located on the parabola x2 = = x
x4, contains a subsequence that
Give an example of an unbounded sequence (r(n)) nEN CR2
(2, 16) and such that x(i)
converges to the limit x = (2, 16) and such that x(i)
#
x() for any i j.
[4 Marks
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