Loans - Understanding the Cost of Borrowing
A loan is an amount of money borrowed from a bank or lender that must be repaid over time, together with interest. Loans fund everything from buying a home to starting a business to covering an emergency – but they always come at a cost. Understanding exactly how that cost is calculated puts you in control.
Key Terms
| Term | Meaning |
|---|---|
| Principal | The original amount borrowed |
| Interest rate | The percentage charged per year (APR) |
| Term | The length of time over which the loan is repaid |
| Monthly repayment | The fixed amount paid each month |
| Total repayment | Monthly repayment × number of months |
| Total interest paid | Total repayment − Principal |
Simple Loan Interest
For a straightforward loan with simple interest:
Total interest = P × R × T
Total repayment = P + Interest
Monthly payment = Total repayment ÷ (T × 12)
Reducing Balance Method
Most bank loans use a reducing balance (or amortisation) method. Each month, interest is charged only on the remaining balance – not the original loan. As you repay, the balance falls, and so does the interest component of each payment. The monthly payment stays fixed, but an increasing share goes to principal and a decreasing share goes to interest.
Monthly Payment Formula
For a loan with monthly reducing balance:
M = P × [i(1+i)n] / [(1+i)n − 1]
Where: M = monthly payment, P = principal, i = monthly interest rate (annual rate ÷ 12), n = total number of monthly payments.
Worked Examples
Interest = 8 000 × 0.06 × 3 = £1 440.
Total repayment = £8 000 + £1 440 = £9 440.
Monthly payment = £9 440 ÷ 36 = £262.22.
i = 0.04 / 12 = 0.003333. n = 25 × 12 = 300.
(1+i)n = (1.003333)300 ≈ 2.7048.
M = 150 000 × [0.003333 × 2.7048] / [2.7048 − 1]
M = 150 000 × 0.009016 / 1.7048 = 150 000 × 0.005289 ≈ £793.40 per month.
2 years: Interest = 5 000 × 0.08 × 2 = £800. Total = £5 800.
5 years: Interest = 5 000 × 0.08 × 5 = £2 000. Total = £7 000.
A longer term lowers monthly payments but increases the total interest paid by £1 200.
Types of Loans
| Loan Type | Typical Use | Typical APR |
|---|---|---|
| Mortgage | Buying a property | 3–6% |
| Personal loan | Car, home improvement | 5–20% |
| Student loan | University fees and living costs | Variable |
| Credit card | Short-term spending | 20–30% |
| Payday loan | Emergency short-term | 100%+ |
Key Takeaways
- Total interest = P × R × T (simple interest method).
- A longer term reduces monthly payments but increases total interest paid.
- Reducing balance loans charge interest only on the outstanding balance.
- Always compare loans using APR – it reflects the true annual cost of borrowing.
Practice Questions
- A loan of £12 000 is taken at 5% simple interest over 4 years. Find the total repayment and monthly payment.
- Compare borrowing £3 000 at 10% over 1 year vs 3 years. Find the total interest in each case.
- A car loan of £9 500 has a monthly payment of £285 for 36 months. Find the total interest paid.
- A credit card charges 24% APR on an outstanding balance of £600. Assuming no repayments, how much is owed after 1 year?
- Which costs more in total: a £20 000 loan at 3% for 15 years or at 5% for 10 years? Calculate the total repayment for each using simple interest.