You can calculate of an amount and add it on, but try doing that ten times in a row without making a mistake. A multiplier is the decimal equivalent of a percentage change used as a factor in multiplication, allowing you to increase or decrease an amount in a single step. To convert any percentage to a decimal, simply divide the percentage by 100.
For a percentage increase, add the decimal to 1 to find your growth multiplier. For example, a increase becomes . For a percentage decrease, subtract the decimal from 1 to find your . For example, an decrease becomes .
Multipliers are commutative, meaning you can multiply them together to find the overall effect of multiple successive percentage changes. A increase followed by a decrease is simply , representing a overall decrease.
Every time you leave money in a savings account, you do not just earn interest on your original deposit — you earn interest on your previously accumulated interest. This is called compound interest, which represents exponential growth. To calculate the final amount efficiently without year-on-year rounding errors, you must use the iterative multiplier formula:
Where:
In OCR exam questions, you will frequently see rates given as per annum (p.a.), which is a Latin term simply meaning "per year".
Mateo invests £4,200 in a savings account paying 3.5% compound interest p.a. Calculate the total value of the investment after 6 years.
Step 1: Calculate the decimal multiplier.
Step 2: Substitute the values into the compound interest formula.
Step 3: Calculate the final amount and round to 2 decimal places (nearest penny).
Why does a brand-new server system lose a massive chunk of its resale value in its first year, but lose much less in its fifth year? This happens because of depreciation, which is the decrease in value of an asset over time. Depreciation operates as exponential decay, meaning the item loses a fixed percentage of its current value each year, not its original value.
To find the value after several years, you use the exact same iterative formula (), but your multiplier will always be less than 1.
A server system is bought for £24,000. It depreciates by 18% each year. Find its value after 4 years, rounding your answer to the nearest pound.
Step 1: Calculate the decay multiplier.
Step 2: Substitute into the formula.
Step 3: Calculate the final value and round to the nearest pound as requested.
Understanding how to use fractions instead of decimals explains why some seemingly impossible non-calculator questions are actually straightforward. OCR requires you to be able to use a fractional multiplier for exact calculations. Instead of a decimal, you express the percentage change as an improper fraction or simplified fraction.
For an increase, place over 100 (e.g., a increase is or ). For a decrease, place over 100. You can then raise this fraction to a power just like a decimal multiplier, keeping all numbers mathematically exact.
An antique vase worth £500 increases in value by 10% each year. Find its value after 2 years without using a calculator.
Step 1: Find the simplified fractional multiplier.
Step 2: Substitute into the iterative formula.
Step 3: Square the fraction and calculate the final value.
You can mathematically travel backwards in time to find out what an investment started at. This is called reverse compound interest. If you know the final amount () and want to find the original principal (), you rearrange the iterative formula by dividing the final amount by the multiplier to the power of .
Students often use 1.4 for a 4% increase (which is actually a 40% increase) instead of the correct decimal multiplier 1.04.
When calculating depreciation, do not multiply the principal by the percentage (e.g., 0.15) — this calculates the loss for one year only, not the new value. Always use a decay multiplier (e.g., 0.85).
In calculation questions, explicitly write down your decimal multiplier before doing any powers (e.g., writing 1.035 earns you the first method mark even if you miscalculate the final answer).
When a question asks for the "total amount of interest earned" or "total value lost", remember to subtract your final answer from the original principal — the formula A = P × mⁿ only gives the total final value.
The compound interest formula is NOT provided on the OCR formula sheet; you must memorize it.
If a Higher tier question asks you to find the number of years (n) an investment takes to reach a target value, examiners expect you to use a trial and improvement approach on your calculator until the amount is reached.
Multiplier
The decimal or fractional equivalent of a percentage change, used as a factor in multiplication to increase or decrease an amount in a single step.
Growth multiplier
A decimal greater than 1 used to calculate a percentage increase.
Decay multiplier
A decimal less than 1 used to calculate a percentage decrease.
Compound interest
Interest calculated on the initial principal plus any interest accumulated from previous periods.
Exponential growth
A process where a quantity increases by a fixed percentage over equal time intervals, leading to faster growth over time.
Principal
The original value of an item or the initial amount of money invested at the start of a time period.
Per annum (p.a.)
A Latin term used in financial calculations meaning "per year".
Depreciation
The decrease in value of an asset over time, treated as an annual percentage decrease (exponential decay).
Fractional multiplier
A percentage change expressed as a fraction rather than a decimal, highly useful for exact values in non-calculator exams.
Reverse compound interest
A mathematical process used to find the original investment or value (principal) when given the final amount after a percentage change.
Put your knowledge into practice — try past paper questions for Mathematics
Multiplier
The decimal or fractional equivalent of a percentage change, used as a factor in multiplication to increase or decrease an amount in a single step.
Growth multiplier
A decimal greater than 1 used to calculate a percentage increase.
Decay multiplier
A decimal less than 1 used to calculate a percentage decrease.
Compound interest
Interest calculated on the initial principal plus any interest accumulated from previous periods.
Exponential growth
A process where a quantity increases by a fixed percentage over equal time intervals, leading to faster growth over time.
Principal
The original value of an item or the initial amount of money invested at the start of a time period.
Per annum (p.a.)
A Latin term used in financial calculations meaning "per year".
Depreciation
The decrease in value of an asset over time, treated as an annual percentage decrease (exponential decay).
Fractional multiplier
A percentage change expressed as a fraction rather than a decimal, highly useful for exact values in non-calculator exams.
Reverse compound interest
A mathematical process used to find the original investment or value (principal) when given the final amount after a percentage change.