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Cost of Borrowing

Time Value of Money

Thomas Edison’s Universal Stock Printer

In 1869, Thomas Edison sold his first successful invention, the Universal Stock Printer, for $40,000. The company who purchased this equipment offered to pay Edison in a single payment or several annual payments. Edison opted for the smarter one-time payment. But why was this the better choice?
The decision Edison faced was an assessment of the time value of money – how much was that money worth to him now vs. later? This principle is based largely on risk.
Since money in your pocket is guaranteed, its value is generally perceived to be less than a promised sum that carries a varying degree of uncertainty. Factors such as time, opportunity cost and the integrity of the individual or company responsible for making payments all contribute to the final value.
This is why we expect to receive interest when we invest money or pay interest when we borrow it. The greater the risk or opportunity cost, the more interest we expect to pay or receive.
The company offering to purchase Edison’s invention made the decision easy for him by asking for longer payment terms without offering any interest to offset the risk.  
How is Interest Calculated?
“Should I use my student loan money to pay off credit card debt?”
Every year at least one first year veterinary student asks this question. It may seem like a simple inquiry but it has a very personal answer. The decision of what to do with borrowed money all comes down to its cost in each scenario. Is the money on the credit card more expensive than the money from the student loan or is it less? Once this question is answered, the decision of what to do with borrowed money is easy.
The cost of money is determined by adding the total interest on the principle (amount borrowed) and any loan origination fees. Total interest is based on the interest rate, period length (time to pay back the money) and the way the interest is calculated (e.g. simple or compound). If the interest is compounded, the compounding frequency will also impact the total cost of borrowing.
Simple Interest
Simple interest is a fixed percentage of the principle (original amount borrowed or invested). If you are borrowing money, simple interest results in a lower cost of money than compound interest at the same interest rate. The following example illustrates the cost of borrowing $3,902 using simple interest.

Example | Simple Interest

Compound Interest
Compound interest adds the accumulated interest to the principle. Simply put, it is interest on interest. This is a good thing if you are investing money because the interest earned is reinvested, resulting in a greater sum generated from the original investment. If you are borrowing money however, compounding or compound interest makes the original loan more expensive.
Federal student loans do not follow the compound interest equation shown below but they are compounded prior to entering repayment. When a loan is compounded, the total interest accumulated during school is added to the original amount borrowed creating a new principle. Compounding also happens when loan repayment programs are changed (e.g. changing from a standard repayment program to an income driven repayment program). 
The following example illustrates the cost of borrowing $3,902 using compound interest (compounded annually).

Example | Compound Interest

Student Loan Interest
Federal student loan interest is calculated using a different equation than simple interest or compound interest. It is calculated by multiplying the principle, the days since a payment was made and an interest rate factor. This means that money borrowed in the first year is much more expensive than money borrowed in years two, three or four.
There are several loan repayment programs available, making it difficult to determine the total cost of borrowing. The following example looks at the cost of borrowing $3,902 in the first semester of veterinary school and repaying that money under the standard 10 year repayment program. To estimate the cost under income driven repayment programs, use the VIN loan repayment simulator at www.vinfoundation.org.

Example | 10 Year Standard Repayment Student Loan Interest

Comparison
The following diagram illustrates the cost of borrowing $3,902 in the first semester of veterinary school and repaying the loan ten years after graduation. 

Cost of Borrowing Comparison

Case Study
Should Our Student Borrow Money to Pay Off Outstanding Credit Card Debt?
Cost of Money | Credit Card
Our student has $10,000 of credit card debt. She is only able to pay the minimum payment amount while in veterinary school but believes that she will be able to pay the total balance her first year out of school.
The credit card’s Annual Percentage Rate (APR) is 24.49%. Our student pays an average minimum monthly payment is $218.96 for a total of 60 months (four years in school plus one year out). Using a credit card payment calculator, the total payment amount, interest paid, principle paid, and outstanding balance at the end of five years was determined (figure 1).

Figure 1. Credit Card Cost of Borrowing

Cost of Money | Student Loan
Now lets look at the cost of borrowing $10,000 in student loans to pay off the credit card debt.
In this example, our student borrows $10,000 in additional students loans the first semester of veterinary school. The student plans to pay back her student loans using the 10 year standard repayment program.
The following example (figure 2) walks through the cost of borrowing with student loans. To reach the total cost, each monthly amount was calculated and summed using Excel.

Figure 2. Student Loan Cost of Borrowing

What Should Our Student Do?
Under these specific conditions, it costs our student $10,724.42 to borrow $10,000 for five years on her credit card or $3,783.30 to borrow that same amount of money for 14 years using student loans (figure 3). This means our student would save a total of $6,941.12 by paying off the credit card on the first day of veterinary school.

Figure 3. Cost of Borrowing Comparison

Putting It All Together
Now let’s assume our student only has $5,000 in credit card debt and she plans to pay off the balance within six months of graduation (before the end of her student loan grace period). 
For the following questions, use a principle amount of $5,000, period of 54 months, APR of 24.49% and a monthly payment amount of $130.
What if the student had an outstanding auto loan instead of credit card debt?
For the following questions use a principle amount of $15,000, a period of 54 months and an interest rate of 4.21%.

Responses

  2. Jack Tribble July 7, 2020

    I feel like most of the time students are told not to pay off credit card debt with student loans, but with no explanation for why. Thank you for taking the time to explain the math behind the situation. Much appreciated @iwidensky !

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