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Student loans

Author:Callum Marshall
Just IMAGINE...so you got accepted to college. Congratulations! Now that you've run around the house and e-mailed everyone you can think of to tell the good news, it may be time to think about how you'll pay for your higher education. Financial Aid experts recommend that you spend a lot of time cobbling together as many grants and scholarships as possible to pay for your education; it's a rare student who gets a free college education! That means considering the implications of a student loan! In this task you will look at how loans work and some of the mathematics behind them.

Question 1

But, before looking at loans you are going to explore the data on the cost of an average 4-year degree in the US depending on the type of school chosen - public or private. What's the difference? The main difference is the source of funding; private schools do not receive US government funding so they must rely on tuition fees to support their school. If you want to know more about the differences, THIS link will help! Your first task is to use the data below to estimate the cost of a college education in the US (either public or private), for the year you would graduate at PSI (assuming you stayed in Kiev of course!), and hence potentially start college. Use GeoGebra for any graphing you do and add your end result in the answer box below.

Question 1 (continued)

According to a recent article, the typical student borrower graduating with the class of 2015 left college with an average debt of $35,051. Based on the information in the article, estimate what a typical student borrower might have had to borrow by the end of their 4-year degree course assuming they started in the same year that you would start.

Paying back what you owe

So, you need to borrow money to pay for your college education, as around 70% of students in the US need to do. This means a student loan! If you need to borrow money for your education, at some point you need to pay it back! In terms of student loans there are a variety of options in terms of how they can be repaid. You can choose the Immediate repayment option where you start to repay your loan immediately very soon after enrolling at college. You can choose an Interest only option where, during the period of your education, you pay off only the interest, so that you avoid having the interest build up over the years and add to the cost of your loan. Or, you choose Full deferral, where you avoid paying anything back till six months after you graduate. In the questions below you will look at how a basic loan repayment system works, assuming that the repayment option is Full deferral as described above.

Question 2

Look at the example shown in the table below. The amount to be repaid is $20,000 with an annual interest rate of 5% and a repayment value of $377.42 per month. The Interest column is the amount of interest that is added each month. Note that interest is added to the starting balance before the payment is deducted. Note: To generate new numbers in the table, begin by dragging cell B6 down by 1 to get the next starting balance, then find the new value for the interest and then the values in the other cells. After how many months will this loan be paid off? Hint: it may be easier to recreate this spreadsheet on Google Sheets - your choice!

Check your answer to Question 2 using the website linked here.

Check your answer to Question 2 using the website linked here.

Check your answer to Question 2 using the website linked here.

https://www.thecalculatorsite.com/finance/calculators/loancalculator.php

Question 3

According to the graph you looked at previously, the average debt in 2015 for a graduating student who had borrowed money was around $35050. If this debt were to be paid off assuming a fixed interest rate of 6% per annum and a monthly repayment of $389.12, CALCULATE how long it would take. Check your result using the loan calculator.

Calculating the repayment amount

Calculating the number of years it takes to pay off a loan is reasonably straightforward, especially with the help of a spreadsheet. However, it is perhaps more natural to want to know the amount you need to pay given the period you want to repay a loan over. This is what you will now explore.

Question 4

Consider the following scenario: I borrow $500 at a fixed interest rate of 12% per annum and wish to repay the loan over a single year. If the monthly repayment amount is "x", EXPLAIN why the expression below represents the balance of the loan at the end of the first month.

Question 5

Find similar expressions for the outstanding debt at the end of months 2, 3, 4 and 5. Simplify your expressions!

Question 6

By consider the expressions you have found so far, i. explain what is happening to the initial value of $500 as the number of months increases. ii. by how much will the initial $500 grow to at the end of the 12 months? iii. describe the series that is generated by the monthly repayment "x". iv. calculate the value of the monthly repayment. v. check your result using the loan calculator above.

Question 7

In Question 1 you estimated the average debt in your year of graduation for a student who had borrowed money for their college education. Show how to calculate the monthly repayment for this debt assuming a fixed interest rate of 5% and a loan period of;       i. 10 years   ii. 15 years   iii. 20 years.

Question 8

For the academic year 2015-16, the tuition fee at Yale was $47 600. The year you graduate from school you take a 3-year course at Yale and need to take out a loan to cover 60% of the tuition fees over the duration of the course. If you pay back the cost of your tuition over a 20 year period, with fees adjusted for inflation, with a fixed interest rate of 4.5%, how much will you pay per month?

This is the assessment rubric

Grade 10_Studentloans_D.pdf

Grade 10_Studentloans_D.pdf

Question 9

Finally, having looked at some of the maths behind how loans work and some of the potential costs involved, please consider the following question which is related to the Global Context of Fairness and development. Is access to a higher education fair or not given the increasing financial demands on students...and is it worth it?

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