How to Pay for College: Understanding College Payments

Understanding how to pay for college is both a life skill and a tested GED math topic. You may be asked to calculate the net cost of tuition after aid, find the total interest on a student loan, or determine monthly loan payments. This lesson breaks down college financing step by step and shows you the math behind each type of payment.

What Are the Main Ways to Pay for College?

College costs are typically covered by a combination of sources. Knowing the difference between money you repay and money you keep is critical:

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• Grants: Free money from the government (e.g., Pell Grant) — no repayment required.
• Scholarships: Free money based on merit, need, or other criteria — no repayment required.
• Work-Study: Part-time campus employment — you earn wages, no repayment.
• Student Loans: Borrowed money that must be repaid with interest after graduation.
• Family Contributions: Money provided by parents or savings accounts.

How to Calculate College Payment Math

1. Find the out-of-pocket cost after free aid

Remaining \(\color{blue}{\text{ Cost } = \text{ Tuition } – (\text{ Grants } + \text{ Scholarships } + \text{ Work }-\text{ Study } + \text{ Family Contributions })}\)

Example: Tuition = $18,000; Grant = $5,000; Scholarship = $3,000; Work-Study = $2,500; Family = $1,500
Free aid total = $5,000 + $3,000 + $2,500 + $1,500 = $12,000
Remaining = $18,000 − $12,000 = $6,000 (covered by a loan)

2. Calculate simple interest on a student loan

\(\color{blue}{\text{ Interest } = \text{ Principal } \times \text{ Rate } \times \text{ Time }}\)   (\(\color{blue}{I = \text{ Prt }}\))

Example: Loan P = $6,000; annual rate \(\color{blue}{r = 5}\)% = 0.05; time \(\color{blue}{t = 4}\) years
Interest = $6,\(\color{blue}{000 \times 0.05 \times 4}\) = $1,200
Total repaid = $6,000 + $1,200 = $7,200

3. Calculate monthly payment

Monthly \(\color{blue}{\text{ Payment } = \text{ Total }}\) \(\color{blue}{\text{ Repaid } \div \text{ Number }}\) of Months

If $7,200 is repaid over 10 years (120 months): Monthly payment = $7,\(\color{blue}{200 \div 120}\) = $60 per month.

Step-by-Step Summary

1. List all sources of aid: grants, scholarships, work-study, family.
2. Add the free-aid sources; subtract from tuition to find the loan amount needed.
3. Use \(\color{blue}{I = \text{ Prt }}\) to find the total interest on the loan.
4. Add \(\color{blue}{\text{ principal } + \text{ interest }}\) for the total repayment amount.
5. Divide by the number of months in the repayment term for the monthly payment.

Watch: Paying for College (Khan Academy)

This Khan Academy video gives an overview of the main ways students pay for college and the tradeoffs between different sources of funding:

Worked Examples

Example 1: James receives a $4,000 grant and a $2,500 scholarship. His tuition is $12,000. How much does he still need to cover?

Free aid = $4,000 + $2,500 = $6,500. Remaining = $12,000 − $6,500 = $5,500.

Example 2: James takes out a $5,500 student loan at 6% simple interest for 3 years. How much total interest does he pay?

I = $5,\(\color{blue}{500 \times 0.06 \times 3}\) = $5,\(\color{blue}{500 \times 0.18}\) = $990. Total repaid = $5,500 + $990 = $6,490.

Example 3: James repays $6,490 over 10 years (120 months). What is the monthly payment?

$6,\(\color{blue}{490 \div 120}\) ≈ $54.08 per month.

Example 4: A student borrows $8,000 at 5% simple interest. She wants to repay it in 5 years. What is the total amount owed and the annual payment?

Interest = $8,\(\color{blue}{000 \times 0.05 \times 5}\) = $2,000. Total = $8,000 + $2,000 = $10,000. Annual payment = $10,\(\color{blue}{000 \div 5}\) = $2,\(\color{blue}{\frac{000}{\text{ year }}}\).

More Practice: Understanding Financial Aid (CFNC)

This video from College for North Carolina walks through the financial aid process and explains how to read your financial aid award letter:

Exercises

1. College tuition is $15,000. A student receives a $6,000 grant and $2,000 in scholarships. How much remains?
2. A student loans $7,000 at 4% simple interest for 5 years. What is the total interest?
3. Using Exercise 2, what is the total repayment amount?
4. If the student in Exercise 2 repays the loan over 10 years (120 months), what is the monthly payment?
5. A school year costs $9,500. Work-study provides $3,000, family contributes $2,000, and a grant covers $1,500. What loan amount is still needed?
6. A $4,000 loan at 5% simple interest is repaid over 4 years. What is the total repayment?

Answers

1. $15,\(\color{blue}{000 – ($6,000 + $2,000)}\) = $7,000
2. I = $7,\(\color{blue}{000 \times 0.04 \times 5}\) = $1,400
3. $7,000 + $1,400 = $8,400
4. $8,\(\color{blue}{400 \div 120}\) = $\(\color{blue}{\frac{70.00}{\text{ month }}}\)
5. $9,\(\color{blue}{500 – ($3,000 + $2,000 + $1,500)}\) = $9,500 − $6,500 = $3,000
6. I = $4,\(\color{blue}{000 \times 0.05 \times 4}\) = $800; total = $4,000 + $800 = $4,800

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Frequently Asked Questions

What is the difference between a grant and a loan?

A grant is financial aid you do not have to repay — it is essentially free money for school. A loan is money you borrow that must be repaid with interest. On the GED, you may need to distinguish them when computing the net cost of college.

What is simple interest and how is it calculated?

Simple interest is calculated on the original principal amount only (it does not compound). The formula is \(\color{blue}{I = \text{ Prt }}\), where P is the principal, r is the annual rate (as a decimal), and t is the time in years. Total amount \(\color{blue}{\text{ owed } = P + I}\).

How do I find the monthly payment from the total repayment?

Divide the total repayment amount by the number of months in the loan term. For example, if the total is $7,200 and the term is 10 years (120 months), monthly payment = $7,\(\color{blue}{200 \div 120}\) = $60.

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