Multipliers & Interest

Video coming soon3 worked examples

Theory

Before you can tackle complex financial questions, you must be completely comfortable converting percentages into decimals and using multipliers. A multiplier allows you to calculate a percentage increase or decrease in a single step on your calculator.

1. Constructing a Multiplier

For an increase: Add the percentage to 100%, then divide by 100 to make it a decimal. (Example: A 4.5% increase means you now have 104.5%. The multiplier is 1.045).
For a decrease: Subtract the percentage from 100%, then divide by 100. (Example: A 12% decrease means you retain 88%. The multiplier is 0.88).

2. Core Financial Terminology

You must be familiar with the specific language used in Higher Applications exam questions:

Capital: The initial, original amount of money that is either invested into savings or borrowed as a loan.
Interest: The money earned as a reward for saving, or the extra fee charged as the cost of borrowing money.
Effective Rate of Interest (ERI): This is the equivalent interest rate for a specified period of time (e.g., per month, per year) regardless of how frequently the interest is actually applied or if the rate varies during that time.

3. Successive Percentage Changes

If an amount of money experiences multiple different percentage changes over time, you do not need to calculate them one by one.

You can find the final balance by taking the starting capital and simply multiplying it by a continuous chain of multipliers in one single calculation.

Worked examples

Example 1

Example 1: Generating Multipliers

Write down the exact decimal multiplier required to calculate the following changes in a single step:

(a) An increase of 7.2%
(b) An increase of 0.85%
(c) A decrease of 16%

(a) $100\% + 7.2\% = 107.2\%$ . Multiplier = 1.072.
(b) $100\% + 0.85\% = 100.85\%$ . Multiplier = 1.0085.
(c) $100\% - 16\% = 84\%$ . Multiplier = 0.84.

Example 2

Example 2: Applying the Effective Rate of Interest (ERI)

Cameron deposits £3,400 into a new savings account. The account offers an effective rate of interest of 0.4% per month.

(a) State the multiplier used to calculate the balance of Cameron's account.

(b) Calculate the exact balance of the account after exactly one month.

(a) An interest rate always represents an increase to savings.

$100\% + 0.4\% = 100.4\%$ . The multiplier is 1.004.

(b) $\text{Balance} = \text{\pounds}3400 \times 1.004 = \text{\pounds}3,413.60$ .

Example 3

Example 3: Successive Interest Rates (Chain Multiplication)

A local charity invests a capital sum of £8,500 into a high-yield savings bond.

In the first year, the effective rate of interest is 3.1%.
In the second year, the effective rate of interest rises to 4.2%.
In the third year, the effective rate of interest drops to 1.5%.

Calculate the total balance of the charity's investment at the end of the 3 years.

We can use a chain of multipliers to calculate the final balance in a single step.

Year 1 multiplier = 1.031
Year 2 multiplier = 1.042
Year 3 multiplier = 1.015

$\text{Final Balance} = \text{\pounds}8500 \times 1.031 \times 1.042 \times 1.015$

$\text{Final Balance} = \text{\pounds}8500 \times 1.089423... = \text{\pounds}9,260.10$ (rounded to the nearest penny).

Ready to practise?

4 Multipliers and Interest questions with answers and video solutions