When comparing savings accounts or investment products, you'll frequently see terms like gross interest and Annual Equivalent Rate, AER.
Both terms refer to the interest rates you'll earn on your savings, but they provide slightly different perspectives, especially when it comes to compounding.
1. Gross interest
Gross interest refers to the simple interest rate applied to your savings, without taking into account any compounding.
It's the rate of interest before tax, but more crucially, it doesn't consider how frequently the interest is added to the balance over time.
Unlike simple interest, which is only calculated on the initial principal, compound
interest helps your money grow faster. The more frequently interest is compounded, the
greater the overall effect, making compound interest a crucial factor in longterm
investments and savings.
2. Formula for gross interest
Gross (or simple) interest is calculated solely on the principal, or the original investment or
loan amount. Unlike compound interest, it does not take into account the accumulated
interest over time. As a result, simple interest leads to slower growth because the
interest is earned only on the principal, not on previously earned interest.
Formula: The formula for calculating simple interest is:
Where:
i = Gross interest, also known as simple interest
P = Principal (initial investment or loan amount)
r = Annual interest rate (as a decimal)
t = Time (in years)
Example: If you invest £1,000 at an interest rate of 5% for 5 years,
the simple interest would be £250 (£1,000 × 0.05 × 5). This would bring the total amount
after 5 years to £1,250.
3. Annual Equivilent Rate (AER)
AER is designed to give a more accurate reflection of how much interest you'll earn on your savings over a year by factoring in the effect of compounding.
It assumes that interest is being paid and added back to the balance periodically, and this added interest will itself start earning more interest.

Interest growth  Over time, the interest you
earn starts to grow on itself, helping your savings grow faster.

True annual return:  AER reflects the actual return on your savings over a year, after considering compounding, and is often higher than the gross rate for accounts that compound interest.

Standardized measure:  AER is a useful comparison tool when evaluating accounts with different interest payment frequencies or structures, as it provides a clearer idea of overall earnings.

Reinvestment of earnings  Reinvesting your
earnings leads to more growth as the reinvested interest starts earning interest
itself.
4. Formula for Annual Equivilent Rate (AER)
Compound interest is calculated using a formula that accounts for the initial principal,
the interest rate, and the frequency with which the interest is compounded. This formula
helps you determine how much an investment or loan will grow over time with compound
interest.
Formula: The formua for calculating compound interest is:
Where:
A = Final amount (principal + interest)
P = Initial, or principal amount
r = Annual interest rate
n = Number of times interest is compounded per year
t = Time, in years
Example:
If your savings account pays a 5% gross interest rate but compounds daily, the AER may be around 5.13%, reflecting the extra interest you earn due to compounding.
5. Impact of compounding frequency on AER
The frequency at which interest is compounded plays a critical role in determining the
total amount of interest earned or paid. Compounding can occur annually, semiannually,
quarterly, monthly, or even daily. The more frequently the interest is compounded, the
higher the overall return or cost.

Annual compounding  Interest is calculated
and added to the principal once a year. This is the simplest form of
compounding.

Quarterly or monthly compounding  Interest is
added more frequently (every three months or monthly), resulting in faster
accumulation compared to annual compounding.

Daily compounding  Interest is calculated and
added every day, which maximizes growth. This method is more commonly used in
credit cards or loans, where it can increase the cost of borrowing.
Try our calculator to explore how compounding frequency impacts the AER or APR. For more
information on compound interest, read our guide
here.
6. Comparison table
Below is a table comparing the key differences between Gross Interest and Annual Equivalent Rate, AER.
Aspect 
Gross Interest 
Annual Equivalent Rate, AER 
Definition 
The interest rate before accounting for compounding. 
The effective annual interest rate after compounding. 
Compounding 
Does not consider the impact of compounding periods. 
Considers compounding, showing the actual return per year. 
Formula 
I = P × r

AER = (1 +
r
n
)
^{nt} − 1

Purpose 
Shows the nominal interest rate before compounding. 
A comparison tool for understanding the true growth of savings over time. 
Use Case 
Useful for knowing the base rate offered by an account. 
Ideal for comparing products with different compounding intervals. 
7. Impact of compound interest on your savings
Let's explore how your initial investment grows over time, breaking down the total
interest into the amount earned directly on your principal and the amount earned from
reinvested interest.
Your initial investment (£):
Annual Equivalent Rate (AER %):