The Interest Rate of a Loan and Associated Factors

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Table of Contents

The variables that affect the interest rate of a loan
Objective of the study
Statement of the problem
Hypothesis
Data collection
Analysis and results
Multiple linear regression model
Conclusion and discussion
Works Cited

The variables that affect the interest rate of a loan

The interest rate of a loan is a major concern to both the borrower and the lender. The interest charged on loans is a source of revenue to the lender. Therefore, the lender will prefer to maximize revenue. On the other hand, the amount of interest charged is a cost to the borrower. Thus, the interest rate on a loan is a key variable to both parties. On the side of the lender, the major concern is how to estimate the rate of interest for each loan application. The other concerns are what variables to include during estimation and how to identify the variables.

Objective of the study

The paper seeks to carry out a study to establish the factors that have an association with the interest rate of a loan and thus can be used to determine the rate of interest. Several statistical tools will be used in the study. Some of the tools are descriptive statistics, correlation analysis, regression analysis and evaluation of the regression equation.

Statement of the problem

It is perceived that the interest rate of loan highly depends on the risk level of the applicant. The level of risk is commonly measured by the amount of income earned by the applicant and the credit worthiness. A number of measures are often used to gauge the credit worthiness of the applicant. The most common measure is the use of FICO score and credit report. Thus, an applicant with favorable periodic income and satisfactory credit rating has less risk and is likely to pay a lower interest rate.

Hypothesis

Null hypothesis (H_o): The interest rate of the loan depends on the level of risk of the individual
Alternative hypothesis (H₁): The interest rate of the loan does not depend onthe level of risk of the individual

Data collection

The analysis is based on secondary data that is obtained from the website of Lending Club (1). The site provides data that contains details of loan applicants such as the amount of the loan applied, funded amount, terms of the loan, the annual income of the individual, number of queries in the last six months, and average FICO score. The data was downloaded on 14^th October 2013. Further, it contains seven variables for 30 people selected randomly.

Interest rate (Y)	Loan amount (X₁)	Funded amount (X₂)	Term of the loan in months (X₃)	Annual income (X₄)	Inquiries in last 6 months (X₅)	FICO score (X₆)
11.86%	12,800	8,925	60	41,000	1	722
6.39%	3,800	3,800	36	146,000	2	787
11.12%	6,000	6,000	36	42,000	0	702
11.86%	6,000	6,000	60	65,000	0	742
13.98%	25,000	15,525	60	97,000	0	717
11.86%	9,000	9,000	60	40,000	2	757
6.76%	6,250	6,250	36	78,000	2	772
11.49%	5,300	5,300	36	47,500	1	707
18.30%	2,000	2,000	36	20,000	1	677
14.72%	3,350	3,350	36	30,000	3	682
7.51%	7,800	7,800	36	48,000	0	737
14.84%	8,000	8,000	36	25,000	2	687
7.88%	10,000	10,000	36	88,000	1	747
10.75%	5,000	5,000	36	26,100	3	712
10.75%	12,000	12,000	36	33,000	0	722
15.21%	4,000	4,000	60	55,000	1	692
7.88%	16,000	12,150	36	62,000	0	752
11.86%	10,000	10,000	36	50,000	2	702
15.95%	25,000	15,775	36	78,000	1	687
16.32%	3,600	3,600	36	39,996	0	662
7.88%	4,000	4,000	60	28,800	0	747
10.75%	6,000	6,000	36	51,996	1	707
7.51%	7,000	7,000	36	44,208	1	807
11.49%	9,000	6,550	60	48,000	0	737
7.88%	7,000	7,000	36	31,000	1	732
10.75%	14,000	12,700	36	72,150	0	737
13.61%	4,500	4,500	36	18,204	0	677
16.82%	7,000	7,000	60	90,000	3	672
14.84%	3,200	3,200	36	20,800	1	667
11.12%	14,000	14,000	36	60,000	0	717

(Source of the data – Lending Club 1)

Analysis and results

Descriptive statistics

The table presented below shows a summary of descriptive statistics for the various variables.

	Interest rate	Loan amount	Funded amount	Term	Annual income	Inquiries	FICO score
Mean	0.12	8553.33	7547.50	42.40	52558.47	0.97	718.83
Standard Error	0.01	1045.05	686.91	1.97	5105.93	0.18	6.58
Median	0.1149	7000	6775	36	47750	1	717
Mode	0.1186	6000	6000	36	78000	0	737
Standard Deviation	0.03	5724.00	3762.38	10.79	27966.35	1.00	36.07
Sample Variance	0.00	32764126.44	14155489.22	116.52	782116788.33	1.00	1300.83
Kurtosis	-0.84	2.90	-0.26	-0.82	2.93	-0.47	-0.12
Skewness	0.15	1.68	0.76	1.11	1.43	0.74	0.47
Range	0.1191	23000	13775	24	127796	3	145

The table shows that there is high deviation from the mean in the amount of annual income, loan amount and funded amount. The median income in the data is $47,750 while the median loan amount is 7,000. The modal interest rate is 11.86%. Finally, the modal FICO score is 737.

Correlation coefficient

Correlation coefficient measures the degree of association between two variables (Verbeek 20). The results of correlation coefficient indicate that there a weak relationship between the interest rate and the other variables. There is a weak positive relationship between interest rate and loan amount (1.44%), the term of the loan (17.93%) and inquiries (14.48%). Further, there is the weak negative relationship between the funding amount (10.73%) and annual income (27.24%). Finally, there is a strong negative relationship between FICO score (85.24%) and interest rate.

Multiple linear regression model

In the analysis, the dependent variable is the interest rate while the independent variables are the amount of the loan applied, funded amount, terms of the loan, the annual income of the individual, number of queries in the last six months, and average FICO score. The regression line can be simplified as shown below.

Y = b₀ + b₁X₁+ b₂X₂+ b₃X₃+ b₄X₄+ b₅X₅+ b₆X₆

Y = Interest rate

X₁ = Loan amount

X₂ = Funded amount

X₃ = Term of the loan

X₄ = Annual income

X₅ = Number of inquiries in the past 6 months

X₆ = FICO score

The theoretical expectations are b₀, can take any value b₁, b₃ and b₅ > 0 (positive) while b_2,b₄ and b₆< 0 (negative). From the results of regression, the regression line can be written as Y = 0.636566224 + 2.06984E-06X1 – 2.37562E-06X2 + 0.000642208X3 – 5.64485E-09X4 + 0.003503609X5 – 0.000765147X6. The intercept value of 0.6366 represents other variables that affect the demand of the commodity but are not included in the model. The positive coefficients imply that if the related variable increases by one unit, the interest rate will increase by the value of the coefficient. On the other hand, the negative coefficients imply that if the related variable increases by one unit, the interest rate will decrease by the value of the coefficient.

Evaluation of regression model

T – test

A t – test is used to evaluate the statistical significance of the explanatory variables (Vinod 33). A two tailed t- test is carried out at 5% significance level.

Null hypothesis: Ho: b_i = 0

Alternative hypothesis: H₁: b_i ≠ 0

The null hypothesis implies that the variables are not significant determinants of demand. The alternative hypothesis implies that variables are significant determinant of demand.

Test of significance for the linear model

The table presented below summarizes the results of the t – tests.

Variable	t – values computed (t at α 0.05 = 1.9432)	Decision
b0	9.62912	Reject
b1	1.180342	Do not reject
b2	-0.90886	Do not reject
b3	2.193376	Reject
b4	-0.04334	Do not reject
b5	1.090189	Do not reject
b6	-7.95958	Reject

Based on the results above, the value of t – calculated is greater than the value of t – tabulated for two variables (term of the loan and FICO score). This implies that rest the two variables are statistically significant in the determination of interest rate at the 5% significance level. The rest of the variables are not statistically significant since the value of t – computed is less than the value of t – tabulated. Therefore, the null hypothesis will not be rejected at the 5% significance level.

F – test of the regression models

The overall significance of the regression model can be evaluated using an F – test (Verbeek 20). The test will be carried out 5% significance level.

Null hypothesis H0: β0 = β1
Alternative hypothesis H1: βj ≠ 0, for at least one value of j

The null hypothesis implies that the overall regression line is not significant. The alternative hypothesis implies that overall regression line is significant. The value of F – computed (16.26047) is greater than the value of F – tabulated (2.5277). Thus, the null hypothesis will be rejected. This implies that the overall linear regression line is significant and can be used in further analysis and predictions.

R-square value

The value of R – square is 80.92% while the value of the adjusted R-square is 75.94%. The high values are an indication of a strong regression line because the explanatory variables explain 80.92% of the variations in the explained variables. The independent variables cannot explain only 19.08% of the variations in the dependent variables.

Conclusion and discussion

The study focused on establishing the factors that have an association with the interest rate of a loan. From the analysis, it is established that the overall regression line is significant. Also, the variables in the regression line explain a large percentage of variations in the explained variable. However, it is also observed that only two variables are statistically significant in the estimation of interest rate. Therefore, the null hypothesis of the research will not be rejected. The implication of the results on the population is that risk level (commonly measured using FICO) is a significant determinant of the interest rate. The results of the sample can be extrapolated to the population. Further, to improve the study, an analyst should include several measures of the risk level of the individual such as debt to income ratio and open credit lines of the individual. This might improve the number of statistically significant explanatory variables. Also, it will also improve the value of R – square. Finally, an example of bias that might exist in the analysis is omitted-variable bias.

Works Cited

Lending Club 2013, Lending Club Statistics. Web.

Mankiw, Gregory. Principles of Economics, USA: Cengage Learning, 2011. Print.

Verbeek, Marno. A Guide to Modern Econometrics, England: John Wiley & Sons, 2008. Print.

Vinod, Hrishikesh. Hands on Intermediate Econometrics Using R: Templates for Extending Dozens of Practical Examples. Hackensack, NJ: World Scientific Publishers, 2008. Print.

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