In Problems solver 65 - 68 , use graphical approximation techniques or an equation solver to approximate the desired interest rate. Express each answer as a percentage, correct to two decimal places. A discount electronics store offers to let you pay for a $1,000 stereo in 12 equal $90 installments. The store claims that since you repay $1,080 in 1 year, the $ 80 finance charge represents an 8 % annual rate. This would be true if you repaid the loan in a single payment at the end of the year. But since you start repayment after 1 month, this is an amortized loan, and 8 % is not the correct rate. What is the annual nominal compounding rate for this loan?
In Problems solver 65 - 68 , use graphical approximation techniques or an equation solver to approximate the desired interest rate. Express each answer as a percentage, correct to two decimal places. A discount electronics store offers to let you pay for a $1,000 stereo in 12 equal $90 installments. The store claims that since you repay $1,080 in 1 year, the $ 80 finance charge represents an 8 % annual rate. This would be true if you repaid the loan in a single payment at the end of the year. But since you start repayment after 1 month, this is an amortized loan, and 8 % is not the correct rate. What is the annual nominal compounding rate for this loan?
In Problems solver
65
-
68
, use graphical approximation techniques or an equation solver to approximate the desired interest rate. Express each answer as a percentage, correct to two decimal places.
A discount electronics store offers to let you pay for a
$1,000
stereo in
12
equal
$90
installments. The store claims that since you repay
$1,080
in
1
year, the
$
80
finance charge represents an
8
%
annual rate. This would be true if you repaid the loan in a single payment at the end of the year. But since you start repayment after
1
month, this is an amortized loan, and
8
%
is not the correct rate. What is the annual nominal compounding rate for this loan?
k
(i) Evaluate
k=7
k=0
[Hint: geometric series + De Moivre]
(ii) Find an upper bound for the expression
1
+2x+2
where z lies on the circle || z|| = R with R > 10. [Hint: Use Cauchy-Schwarz]
4.
5.
6.
Prove that p (gp) is a tautology using the laws of propositional logic.
Prove that p((pVq) → q) is a tautology using the laws of propositional logic.
Let us say a natural number n is ok if there are two natural numbers whose sum
is n and whose product is n. (Convention: the natural numbers consist of 0, 1, 2,...)
(a) Give a logical expression that means "n is ok".
(b) Show that 0 and 4 are both ok.
(c) Give a logical expression that means "every natural number is ok".
(d) Give a logical expression that means "it is not the case that every number is ok". Push
the negations into the expression as far as possible.
7.
Let E(x, y) be a two-variable predicate meaning "x likes to eat y", where the
domain of x is people and the domain of y is foods. Write logical expressions that represent
the following English propositions:
(a) Alice doesn't like to eat pizza.
(b) Everybody likes to eat at least one food.
(c) Every student likes to eat at least one food other than pizza.
(d) Everyone other than Alice likes to eat at least two different foods.
(e) There are two different people that like to eat the same food.
Chapter 3 Solutions
Finite Mathematics for Business, Economics, Life Sciences and Social Sciences Plus NEW MyLab Math with Pearson eText -- Access Card Package (13th Edition)
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