By J. J. McCutcheon and W. F. Scott. | An Introduction to the Mathematics of Finance. By McCutcheon J. J. and Scott W. F.. - Volume Issue 3 - Simon Carne. This book is a revision of the original An Introduction to the Mathematics of. Finance by J.J. McCutcheon and W.F. Scott. The subject of financial. for the subject CT1 (Financial Mathematics) of the Actuarial Profession. The .. in financial mathematics the profitability of an investment for a short period of time of [2] J.J. McCutcheon, W.F. Scott. An Introduction to the Mathematics of Fi-.

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Introduction to the Mathematics of Finance 2ed [] - Ebook download as PDF File .pdf), Text File .txt) or read book online. book is necessarily mathematical, but I hope not too mathematical. Finance by J.J. McCutcheon and W.F. Scott. mathematics of finance. We calculate an accumulated amount of some special im - mediate annuities by solving the special type of non-homogenous linear. An Introduction to the Mathematics of Finance: A Deterministic Approach P.D.F. This revision of the McCutcheon-Scott classic follows the core.

Specifically, we conducted a latent profile analysis LPA , thereby inferring three homogeneous subgroups of individuals or latent classes from their response patterns on the item sources of math self-efficacy measure. Our findings support the importance of math self-efficacy in choice of major as well as overall academic performance regardless of whether a student is in a STEM field or a non-STEM field. Researchers suggested that the difference between Asian students and students of other minority groups in STEM representation may be due to the fact that Asian students are often better prepared in high school mathematics Berkner and Choy, Additionally, compared with students who took calculus or other advanced math courses during their first year of college, those who took introductory math courses had a higher probability of switching out of STEM majors Chen, Students with high grades in middle school mathematics were shown to have increased likelihood of being attracted to STEM at the end of high school Sadler et al. General research also converges in agreement that math achievement is directly associated with entrance, persistence, and success in STEM e. Theoretical Framework: Social Cognitive Career Theory Based on the fundamental assumption of social cognitive theory that behaviors are derived from the interplay of person predispositions and the environment Bandura, , Lent et al. Individuals are more likely to make educational and occupational choices that are consistent with their self-efficacy and interests, particularly if accompanied by favorable environmental or contextual variables Lent et al. Social cognitive career theory regards self-efficacy as the central variable that predicts career outcomes, such as interests, intentions, and goals.

Time value of money. Rate of interest, rate of discount, and force of interest. Accumulated values and discounted values. Accumulation and discounting of a possibly infinite cash flow to a given time, where both the rate of cash flow and the force of interest may be time-varying.

Nominal rates, effective rates, rates payable multiple times per annum. Equation of value for a cash flow problem, and methods of solution. Equation of value corresponding to periodic repayment of a loan. Interest and capital content of annuity payments where the annuity is used to repay a loan.

Consumer credit transactions.

Real rate of return in presence of inflation. Expected utility theory, prospect theory, framing, heuristics, and biases. The Bernartzi and Thaler solution to the equity premium puzzle. The measure consisted of six items, two of which were reverse-coded.

Higher scores indicate higher orientation and more welcoming attitude toward other groups. Higher scores indicate that participants have higher interest in STEM subjects. The majors that were coded as 1 include all majors in the engineering college, mathematics department, chemistry department, biology department, physics department, and computer science department.

For example, psychology and anthropology were assigned a numeric code of 2. Majors that are lowest in STEM content, such as those in the fine arts college, journalism college, English department, and foreign language department were given a numeric code of 3. The process of coding began with consultation of a variety of STEM taxonomies, such as those listed by the National Science Foundation, National Institutes of Health, and Institutional Research and Report office of the university in which the study was conducted.

A team of researchers, including two of the authors of the current study and two additional graduate research assistants, created the Major-to-STEM Code key by sorting every major that was offered at the university into the three STEM categories. In the final step, the two undergraduate research assistants and two graduate research assistants discussed the majors in question and reached consensus.

In the sample to which the final model was fitted, of the participants were assigned a STEM code of 1, 81 of the participants were assigned a STEM code of 2, and of the participants were assigned a STEM code of 3. Retention GPA is a cumulative summation of grades from all classes that a student has taken on a 4-point scale. It was used by the University in administrative policies and thus was regarded as a justified comparative metric across students of different academic majors.

The average retention GPA for the students that were included in the final model was 3. Analysis Conducting Latent Profile Analysis In the first step, we conducted latent profile analyses using the 18 items in the math self-efficacy scale.

Based on recommended procedures in Masyn , we fitted a series of models with a varying number of latent classes. We selected the model that provides not merely adequate representation of the data but also substantively meaningful interpretation of the identified latent classes. We assumed that the covariances among the indicators within a class were zero. We allowed the variances to differ across classes, thereby allowing some classes to be more heterogeneous than other classes with respect to the responses to the observed variables Hagenaars and McCutcheon, Model parameters were estimated by EM algorithm, and the associated standard error estimates were obtained by the robust or the sandwich estimator Collins and Lanza, Furthermore, the substantive quality of the latent profile model solution can be assessed by entropy, proportion of the smallest class, class homogeneity, class separation, and posterior probability see Hagenaars and McCutcheon, ; Marsh et al.

We followed the recommendations in Masyn for the evaluation of model fit and substantive quality in the evaluation and selection of the model. Latent Class Model With Covariates and Outcomes Adding covariates in the model to predict the latent class membership essentially involves conducting a multinomial logistic regression analysis to predict probability for each category of the dependent variable. The estimated intercepts and regression coefficients are transformed into odds and odds ratios, respectively, by using exponential function.

The exponentiated intercept represents the odds of membership in one class relative to the reference class when all covariates are equal to 0. The exponentiated regression coefficient of a covariate represents the change in odds of membership in one class relative to the reference class when the covariate is changed by one unit, holding other covariates constant.

The continuous variables i.

In the analysis of outcomes for the current LPA model, we examined how class membership predicts the outcome variables of interest. In the first step, participants were categorized into latent classes based on their highest posterior probability of being in a given class. In the second step, one would create a new data file that contains the class assignments.

In the last step, one would regress the outcome variables on the most likely class membership. In the regression model, STEM code was treated as a nominal variable.

The STEM code of 2 was used as the reference. All statistical analyses were conducted in Mplus Version 7.

Supplementary Figure 2 displays the final list of predictors and outcomes. Results The descriptive statistics and correlations for the predictor variables are presented in Supplementary Table 1. The inter-item correlations for the sources of math self-efficacy measure are presented in Supplementary Table 2. Results of Latent Profile Analysis To decide on the number of classes, we compared models with between one and four classes using a variety of statistical fit indexes, including information criteria, LMR-LRT, entropy, and the size of the smallest class.

The LMR-LRT also indicated that there was no improvement in fit for the inclusion of one more class to the three-class model i. Moreover, the size of the smallest class in the four-class model was zero.

Entropy was the highest for the three-class model, which indicates that individuals were classified into latent classes more accurately in the three-class model than in the other models.

More importantly, the three-class model offered much clearer substantive interpretability than the four-class model. Thus, we selected the three-class model as the final model. The profiles for the three-class model are presented in Supplementary Figure 3.

The mean posterior probability of a member classified in the Mastery group to belong to the Mastery group was 0. The mean posterior probability of a member classified in the Moderate group to belong to the Mastery group was 0. The mean posterior probability of a member classified in the Unconfident group to belong to the Mastery group was 0. In other words, the two models have no practical difference in the estimated class posterior probabilities for each individual. Minor differences could be due to the reduction of sample size in the model with covariates.

Because of missing data in the covariates, the sample size in the model with covariates changed from to Predictors of Latent Classes The results for the effects of the predictors of the latent classes were estimated as the odds of 1 membership in the Unconfident group relative to the Moderate group, 2 membership in the Mastery group relative to the Moderate group, and 3 membership in the Unconfident group relative to the Mastery group.

Unconfident moderate as reference The odds coefficients were significant for the intercept and two of the four predictorsâ€”Native American and ITMA see Supplementary Table 4. The estimate of the intercept indicated that when all predictors were equal to 0, the odds of membership in the Unconfident group relative to the Moderate group was 0. It should be noted that all continuous predictors were standardized, such that the mean of each variable equaled 0.

Therefore, the intercept estimate of 0. As shown in Supplementary Table 4 and Supplementary Figure 4 , for one unit increase in Native American, the odds of membership in the Unconfident group relative to the Moderate group increased by a factor of 2. That is, participants who indicated higher agreement to the view that math ability is fixed are more likely to belong to the Unconfident group in comparison to the Moderate group.

In order to understand the nature of the interaction between OGO and ITMA, we plotted the impacts of ITMA on the odds of membership in the Mastery group relative to the Moderate group when OGO was one standard deviation below the mean, at the mean, and one standard deviation above the mean. As shown in Supplementary Figure 5 , when OGO was one standard deviation below the mean, for one standard deviation increase in ITMA, the odds of membership in the Mastery group relative to the Moderate group was 0.

This value was 0. However, when OGO was one standard deviation above the mean, the odds of membership in the Moderate group and Mastery group were about one-to-one the reciprocal of 0. Thus, the effects of ITMA may be more relevant in determining membership in the Mastery group relative to the Moderate group when the person has a weaker orientation to other ethnic groups.

The intercept indicated that when all four predictors were equal to 0, the odds of being in the Unconfident group relative to the Mastery group was 0. As shown in Supplementary Table 4 and Supplementary Figure 4 , when participants indicate that they are part Native American, the odds of being in the Unconfident group relative to the Mastery group increased by a factor of 2. This value was 3.

In other words, higher endorsement of the belief that math ability is fixed was associated with a higher chance of belonging to the Unconfident group rather than the Mastery group. Membership in the Moderate group was used as the reference group.

Full Information Maximum Likelihood FIML was used to treat missing data due to the denial of access to academic records such that the sample size of the model remained at Interestingly, neither membership in the Unconfident group nor membership in the Mastery group significantly predicted the odds of having a non-STEM major. This suggests that, while the latent class membership based on math self-efficacy predicted the odds of having a STEM major, it did not predict the odds of choosing a non-STEM major.

Discussion Research continues to point out problems in the selection and retention of various minority groups in STEM fields Fouad and Santana, We first conducted a LPA with covariates to identify subgroups of individuals who share similar response patterns to the sources of math self-efficacy measure, and then utilized the identified subgroup membership to predict interest in STEM subjects, interest in STEM-related activities, choice of STEM major, and overall retention GPA.

Results from the LPA model supported a three-class model. That is, based on their response patterns to the item math self-efficacy measure, three distinct subgroups of individuals were present in the current sample. Page Count: Sorry, this product is currently out of stock. Flexible - Read on multiple operating systems and devices. Easily read eBooks on smart phones, computers, or any eBook readers, including Kindle.

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Theory of Interest Rates 2. The Basic Compound Interest Functions 3. Further Compound Interest Functions 4. Present Values and Accumulations 4. Loan Repayment Schedules 5. Project Appraisal and Investment Performance 6. The Valuation of Securities 7. More Complicated Examples 7. Capital Gains Tax 8.