What is gross interest?

Gross interest is the total interest earned on a savings account or investment before tax deductions. It represents the simple interest rate and does not take into account any compounding.

What is AER (Annual Equivalent Rate)?

AER stands for Annual Equivalent Rate and reflects the total interest you would earn in one year, taking into account the effect of compounding. It shows how much you would earn if interest is paid back into the account, allowing for compounding.

How is AER different from gross interest?

While gross interest is the rate without considering compounding, AER reflects the real growth of savings, including the impact of compounding. AER is usually higher than the gross rate for accounts that compound interest.

How do compounding frequencies affect AER?

The more frequently interest is compounded (e.g., daily, monthly), the higher the AER will be compared to the gross interest rate. This is because interest is added back to the balance more often, allowing for more growth.

How do I calculate AER from gross interest?

To calculate AER from the gross interest, use the formula: AER = (1 + r/n)^(n) - 1, where r is the gross interest rate and n is the number of compounding periods per year.

OPTIMLY Guides | Gross interest and AER Guide

Gross interest and AER

Overview

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 long-term 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:

i = P × r × t

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:

A = P ( 1 + r n ) ^nt

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, semi-annually, 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.

Calculator:

Try our calculator to explore how compounding frequency impacts the AER or APR. For more information on compound interest, read our guide here.

Enter gross rate (%):

Compound frequency:

Annual rate (AER/APR %):

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 %):

Show years: