How to Calculate Gross Interest (Step-by-Step Guide with Examples)
What is Gross Interest?
Gross interest is the total amount of interest earned on an investment or deposit before any deductions are made (such as taxes and fees).
This contrasts with net interest, which is the amount remaining after deductions.
For example, if you were to earn £1,000 in gross interest on a savings account, but there is a tax of 20%, the net interest would be £800.
Gross interest calculations are often used when preparing financial statements or evaluating investment returns, as they provide a baseline for comparison.
Gross interest is important for understanding the real value of an investment, as it shows the total earnings before accounting for any charges.
Simple Interest vs Compound Interest
It is important to note that the type of interest will affect how gross interest is calculated.
More specifically, simple interest or compound interest.
Simple interest is the more straightforward calculation and accumulates on the initial principal only.
Compound interest, however, is calculated on the initial principal plus any accumulated interest, meaning the investment grows faster due to earning “interest on interest.”
Gross Interest Formulas
The formulas to calculate gross interest are different depending on whether we’re dealing with simple or compound interest:
Simple Interest Formula
For investments with simple interest, gross interest can be calculated using the formula:
Gross Interest = P × R × T
Where:
P = Principal amount (initial investment)
R = Interest rate (annual, expressed as a decimal)
T = Time period in years
Compound Interest Formula
For investments with compound interest, gross interest can be calculated using the formula:
Gross Interest = P × (1 +(R/N))n×T − P
Where:
P = Principal amount (initial investment)
R = Interest rate (annual, expressed as a decimal)
T = Time period in years
n = Number of times the interest is compounded per year
Simple Interest Example
If you invest a lump sum of £1,000 at a simple interest rate of 5% for 3 years, the calculation would be:
Gross Interest = P × R × T
Gross Interest = £1,000 × 0.05 × 3 = £150
So, the gross interest earned over 3 years would be £150.
Compound Interest Example
Using the same example, £1,000 with a 5% annual interest rate compounded annually over 3 years:
Gross Interest = P × (1 +(R/N))n×T − P
Gross Interest = £1,000 × (1 +(0.05/1))1×3 – P = £157.63
So, the gross interest earned over 3 years with compound interest is £157.63.
Step-by-Step Guide to Calculating Gross Interest
Here’s a step-by-step approach to calculating gross interest for both simple and compound interest investments.
Step 1: Determine the Principal Amount (P)
Identify the principal amount invested or deposited.
This is the base amount on which interest will be calculated.
Step 2: Identify the Interest Rate (R)
Identify the annual interest rate and the convert percentages into decimals for the calculation – ie 5% = 0.05.
Step 3: Determine the Time Period (T)
Identify the time period the investment will be held, in years.
Step 4: If Applicable, Determine Compounding Frequency (n)
If the investment uses compound interest, identify the compounding frequency:
- Annually, n = 1
- Semi-annually, n = 2
- Quarterly, n = 4
- Monthly, n = 12
Step 5: Apply the Appropriate Formula
For simple interest, use:
Gross Interest = P × R × T
For compound interest, use:
Gross Interest = P × (1 +(R/N))n×T – P
Step 6: Solve Formula for Gross Interest
Plug the values into the formula, and calculate the gross interest.
Real World Examples of Gross Interest Calculations
Let’s apply the formulas to a couple of real world examples:
Example 1: Simple Interest Investment
Sarah invests £2,000 into a bond with a simple interest rate of 4% for 5 years.
The gross interest she will earn can be calculated as:
Gross Interest = P × R × T
Gross Interest = £2,000 × 0.04 × 5 = £400
So, Sarah will earn £400 in gross interest after 5 years.
Example 2: Compound Interest Investment
Mike is saving for a deposit on a new house.
He deposits £10,000 in a savings account with an interest rate of 6%, compounded quarterly, for 10 years.
The gross interest he will earn can be calculated as:
Gross Interest = P × (1 +(R/n))n×T − P
Gross Interest = £10,000 × (1 +(0.06/4))4×10 – P = £8,140.18
This gives Mike £8,140.18 in gross interest over 10 years, meaning he will now have £18,140.18 towards his house deposit.
How to Calculate Gross Interest from AER (Annual Equivalent Rate)
AER, or Annual Equivalent Rate, is an interest rate that accounts for the effects of compounding over a year.
AER shows the real rate of return on an investment or deposit, providing an accurate yearly interest rate even when interest compounds more frequently than once a year.
Some accounts calculate interest annually, while others compound bi-annually, quarterly, monthly or even daily.
The frequency of compounding affects how much interest you actually earn.
For example, if one account offers 10% interest compounded annually, £100 will grow to £110 by the end of the year.
However, if another account offers 5% interest compounded semi-annually, that £100 earns 5% (£5) after six months, and then another 5% on the new total (£105), ending the year at £110.25.
That extra £0.25 is due to compounding.
The AER reflects the total return over a year, taking into account both the interest rate and the compounding frequency.
This allows for a fair comparison between accounts, even if they compound interest at different intervals.
When calculating gross interest from AER, we can use it directly as the annual rate if the investment period is exactly one year.
However, for periods shorter than a year or for custom calculations, we’ll break down the process step-by-step.
Formula for Calculating Gross Interest from AER
The formula for calculating gross interest from AER is:
Gross Interest = P × ((1 + AER / 100)T / 1−1)
Where:
P = Principal (initial amount invested)
AER = Annual Equivalent Rate (expressed as a percentage)
T = Time period in years (for example, 0.5 for 6 months)
Step-by-Step Guide to Calculating Gross Interest from AER
Let’s look at two examples, one with an investment held for less than a year, and the other for an investment held for exactly one year.
Investment Held For Less Than a Year
Imagine we have invested £10,000 in a savings account with an AER of 3.5%, and want to calculate the gross interest earned in six months.
Using the formula:
Gross Interest = P × ((1 + AER / 100)T / 1−1)
We need to identify P, AER and T:
P = £10,000
AER = 3.5%, or 0.035
T = 0.5 (ie half a year)
So, Gross Interest = £10,000 × ((1 + 0.035 / 100)0.5 / 1−1)
Therefore, the gross interest earned over six months is £173.73
Investment Held For Exactly a Year
For investments held for exactly one year, calculating gross interest from AER is straightforward:
Gross Interest = P × (AER / 100)
For example, with a £10,000 investment at a 3.5% AER over one year, the gross interest would be:
Gross Interest = P × (AER / 100)
Gross Interest = £10,000 × (3.5 / 100)
So, the gross interest earned in one year would be £350.
How to Calculate Gross Interest from Net Interest
There may be instances where we know the net interest, but want to calculate the gross interest.
To do this, we need to know the tax rate (or any other deduction) percentage applied to the interest income.
The formula for calculating gross interest from net interest is:
Gross Interest = Net Interest / [1 − Tax Rate]
Where:
Net Interest = Interest amount after tax or deductions
Tax Rate = Percentage of interest taken as tax (expressed as a decimal)
For example:
Assume your net interest on a deposit is £300, and you know a 20% tax was applied.
To find the gross interest, we would calculate:
Gross Interest = Net Interest / [1 − Tax Rate]
Gross Interest = 300 / [1 − 0.20] = £375