A mortgage is a long-term loan for property; a personal loan covers smaller purchases. Both charge interest, so you repay more than you borrowed. At GCSE, questions ask you to find the total repayment, total interest paid and to compare two loan deals.
Key vocabulary for loan problems
| Term | Meaning |
|---|---|
| Principal | The amount originally borrowed |
| Interest | The extra amount charged for borrowing |
| APR | Annual Percentage Rate — the yearly interest rate |
| Term | The length of the loan (e.g. 3 years, 25 years) |
| Monthly repayment | Fixed amount paid each month |
| Total repayment | Monthly payment × number of months |
| Total interest | Total repayment − amount borrowed |
How do you calculate total repayment and total interest?
Worked example 1 — fixed monthly payment:
Kezia takes out a loan of £6000 over 3 years. She pays £192 per month. Find the total repayment and total interest paid.
Total repayment: £192 × 36 = £6912
Total interest: £6912 − £6000 = £912
This is the most common type of GCSE question — the monthly payment is given and you simply multiply.
Worked example 2 — simple interest loan:
A loan of £4500 is offered at 6% per annum simple interest for 2 years. Find the total repayment.
Interest per year: 6% × £4500 = £270
Interest over 2 years: £270 × 2 = £540
Total repayment: £4500 + £540 = £5040
How do you compare two loan deals?
GCSE problems often present two options (different interest rate, different term, or different monthly payments) and ask which is cheaper overall, or by how much.
Worked example 3:
Liam borrows £3600. Two deals are offered:
Deal A: 15% per annum simple interest, repaid over 2 years in equal monthly instalments.
Deal B: Fixed monthly payment of £175 for 2 years.
Deal A:
Interest = 15% × £3600 × 2 = £1080
Total = £3600 + £1080 = £4680
Monthly payment = £4680 ÷ 24 = £195
Deal B:
Total = £175 × 24 = £4200
Deal B is cheaper. Savings: £4680 − £4200 = £480.
How do compound interest loans work at GCSE?
Some loan questions use compound interest — each year's interest is added to the outstanding balance and interest is charged on the new total. GCSE questions of this type usually give you the annual rate and number of years and ask for the total amount owed.
Worked example 4:
A mortgage of £180,000 is taken at 3.5% per annum compound interest for 2 years. No repayments are made in this period. Find the amount owed after 2 years.
Year 1: £180,000 × 1.035 = £186,300
Year 2: £186,300 × 1.035 = £192,820.50
Amount owed: £192,820.50
Interest paid: £192,820.50 − £180,000 = £12,820.50
Compare with simple interest: £180,000 × 3.5% × 2 = £12,600 — compound interest costs £220.50 more.
What is APR and how is it used at GCSE?
APR stands for Annual Percentage Rate. In the real world, APR standardises how lenders advertise costs so that borrowers can compare fairly. At GCSE, APR is treated as the annual interest rate in percentage form and is used in exactly the same way as any other interest rate — either as a simple or compound rate, depending on how the question frames it.
Worked example 5 — choosing the best deal using APR:
| Loan | Amount | APR | Term |
|---|---|---|---|
| Deal X | £5000 | 8% simple per year | 3 years |
| Deal Y | £5000 | 6% compound per year | 3 years |
Deal X total interest: 8% × £5000 × 3 = £1200 → total = £6200
Deal Y total: £5000 × 1.06³ = £5000 × 1.191016 = £5955.08
Deal Y is cheaper by £6200 − £5955.08 = £244.92, even though it uses compound interest.
Frequently asked questions
Will GCSE always give me the monthly payment, or do I have to work it out?
For mortgages and longer loans, the exam usually provides the monthly payment or a repayment table — calculating mortgage repayments from scratch requires the compound interest annuity formula, which is beyond GCSE. For simple interest loans, you calculate total interest, add to the principal and then divide by the number of months.
What is the difference between APR and AER?
APR (Annual Percentage Rate) is used for loans; AER (Annual Equivalent Rate) is used for savings. Both represent the annual rate, but they account for compounding differently. At GCSE, you will see APR for loan questions and will treat it as the annual interest rate.
Should I include any deposit when calculating total cost?
Yes, if a deposit is required. The total cost of borrowing = deposit + total repayment (all monthly payments). The interest is only charged on the amount borrowed (after the deposit), not the full price. Subtract the deposit from the purchase price to find the principal before applying the interest formula.
How do I show which deal is better in an exam answer?
Calculate the total repayment for each deal, compare, and state a clear conclusion: "Deal B is cheaper overall by £480, so Liam should choose Deal B." Always back up your recommendation with calculations and a numerical comparison.
Work through GCSE financial maths questions with Professor Pi at aitutors.me.