In Problems 47 - 50 , 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 person makes annual payments of $ 1 , 000 into an ordinary annuity. At the end of 5 years, the amount in the annuity is $ 5 , 840 . What annual nominal compounding rate has this annuity earned?
In Problems 47 - 50 , 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 person makes annual payments of $ 1 , 000 into an ordinary annuity. At the end of 5 years, the amount in the annuity is $ 5 , 840 . What annual nominal compounding rate has this annuity earned?
In Problems
47
-
50
, 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 person makes annual payments of
$
1
,
000
into an ordinary annuity. At the end of
5
years, the amount in the annuity is
$
5
,
840
. What annual nominal compounding rate has this annuity earned?
Refer to page 100 for problems on graph theory and linear algebra.
Instructions:
•
Analyze the adjacency matrix of a given graph to find its eigenvalues and eigenvectors.
• Interpret the eigenvalues in the context of graph properties like connectivity or clustering.
Discuss applications of spectral graph theory in network analysis.
Link: [https://drive.google.com/file/d/1wKSrun-GlxirS3IZ9qoHazb9tC440 AZF/view?usp=sharing]
Refer to page 110 for problems on optimization.
Instructions:
Given a loss function, analyze its critical points to identify minima and maxima.
• Discuss the role of gradient descent in finding the optimal solution.
.
Compare convex and non-convex functions and their implications for optimization.
Link: [https://drive.google.com/file/d/1wKSrun-GlxirS31Z9qo Hazb9tC440 AZF/view?usp=sharing]
Refer to page 140 for problems on infinite sets.
Instructions:
• Compare the cardinalities of given sets and classify them as finite, countable, or uncountable.
•
Prove or disprove the equivalence of two sets using bijections.
• Discuss the implications of Cantor's theorem on real-world computation.
Link: [https://drive.google.com/file/d/1wKSrun-GlxirS31Z9qoHazb9tC440 AZF/view?usp=sharing]
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