Finance · Topic 5 of 5
Saving & Borrowing
Theory
The Golden Rule: When an exam question asks you to determine which of two investment or savings options is best, you must clearly calculate the final total value for both options to make a valid comparison.
1. Simple Interest
Simple interest is calculated purely on the original amount invested or borrowed. To calculate it, you find one year's interest using basic percentages, and then multiply that amount by the total number of years:
where is the amount invested or borrowed, is the percentage rate per year, and is the number of years.
2. Compound Interest (Appreciation)
Compound interest is a form of appreciation where the amount in the account is always going up, so the interest you earn grows each year.
- You should always use the "quicker method" involving a decimal multiplier and a power.
- For example, an investment of £2500 at a rate of 2.4% over 3 years is calculated in one step: .
- Using the "longer method" of calculating year-by-year becomes totally impractical over long time periods.
3. Loans & Repayments
When taking out a loan, you must pay back the original amount borrowed plus an additional interest charge or administration fee.
- Step 1: Calculate the total interest and fees.
- Step 2: Add this to the original loan amount to find the total amount repayable.
- Step 3: Divide this new total by the number of months to find the equal monthly repayments.
4. Annual Percentage Rate (APR) & Credit
APR is a standardised calculation used to compare different loans and credit cards. Because it includes both the interest rate and any mandatory fees, looking for the lowest APRs is the most accurate way to find the true, overall cost of borrowing.
5. Hire Purchase
Hire purchase lets you have an item straight away and pay for it in instalments, instead of saving up the full cash price. The convenience almost always costs more overall.
A plan is usually made of a deposit (often a percentage of the cash price), a number of monthly instalments, and sometimes a final payment. Total them all, then compare with the cash price:
6. Shares
A company can raise money by selling shares. Buying one makes you a shareholder, owning a small piece of the company. Share values rise and fall with the company's fortunes, so buying shares can produce a profit or a loss — it is not a guaranteed return like a savings rate.
The calculation is always the same: total what was paid, total what was received, and compare.
If the shares were bought and sold at a single price each, the percentage profit can be found from one share alone, since the proportion is the same however many were held.
⚠️ Common Examiner Traps
- The "Interest vs Balance" Trap: When comparing a compound interest savings account with a fixed-interest bond, candidates frequently calculate the total balance for one option but only the interest gained for the other. Ensure you add the interest to the original investment for OptionB so you are comparing total value against total value.
- The "Year-by-Year" Trap: For compound interest over multiple years (e.g., 15 years), doing 15 lines of calculations is a massive trap that wastes time and causes rounding errors. Always use a multiplier and a power.
- The "Missing Addition" Loan Trap: When asked to calculate a monthly loan repayment, candidates often calculate the administration fee and immediately divide only the fee by the number of months, forgetting to add the original loan amount back on first.
Worked examples
Example 1
David has £4000 which he will invest for 3 years. He is considering two options:
- Savings account: Interest rate of 3.2% per annum.
- Stocks and shares ISA: 3-year investment guaranteed £95 interest for every £1000 invested.
Determine which option will have the greater value after 3 years. Use your working to justify your answer. (4 marks)
Step 1 (Savings Account): Use the compound interest multiplier for a 3.2% increase (1.032) over 3 years.
Total value for Savings Account = £4396.16.
Step 2 (ISA): Calculate how many "lots" of £1000 David has.
Total interest =
Total value for ISA =
Step 3 (Conclusion): Compare the total values. The Savings Account will have the greater value (£4396.16 > £4380.00).
Example 2
Sarah takes out a loan of £6500. The interest plus the administration fee is 8.5% of the loan amount. The total amount will be paid back in 12 equal monthly payments. Calculate her monthly payment. (3 marks)
Step 1: Calculate the total interest and administration fee.
Step 2: Add the fee to the original loan find the total amount repayable.
Step 3: Divide the total amount by 12 to find the monthly repayment.
Final Answer: Rounded to exactly two decimal places for money, the monthly payment is £587.71
Example 3
Hire Purchase
A washing machine has a cash price of £480. It can also be bought on a payment plan:
- a deposit of 15% of the cash price
- 12 monthly instalments of £38
Calculate how much more expensive the payment plan is than paying cash.
Step 1: Work out the deposit — 15% of the cash price:
Step 2: Work out the total of the instalments:
Step 3: Add them for the total cost of the plan:
Step 4: Compare with the cash price:
Answer: the payment plan costs £48 more than paying cash.
Example 4
Shares (profit or loss)
Jamila bought 400 shares in a company at £3.15 each. She later sold 250 of them at £3.80 each, and the remaining 150 at £2.90 each.
Calculate her overall profit or loss, before any charges.
Step 1: Calculate the total buying price:
Step 2: Calculate the total selling price. The shares were sold in two batches at different prices, so work out each and add:
Step 3: Compare the two totals. She received more than she paid, so this is a profit:
Answer: Jamila made a profit of £125.