What it means
When you see 6% pa on a loan, it means the interest rate is 6% for a full year. A salary of $80,000 pa means $80,000 across the year.
The label is used to avoid confusion when amounts are quoted for different periods such as weeks, months or quarters. The label matters most with interest.
A rate quoted per annum is not the same as what you actually pay if interest is charged more often. A loan at 12% pa charged monthly adds 1% each month, and because each month's interest is added to the balance, the true yearly cost is higher than 12%.
This is why finance professionals distinguish between the nominal rate and the effective annual rate. The nominal rate is the stated pa figure, while the effective rate includes the effect of compounding, which is interest earning interest.
Comparing products fairly means comparing effective rates over the same period. Converting amounts is a daily task.
A monthly figure is multiplied by 12 to give an annual one, and a weekly figure by 52, although day-count rules in loan agreements can vary. A salary of $5,000 a month is $60,000 pa.
Be careful with other meanings. In legal and business settings PA can mean power of attorney, personal assistant, public accountant or purchasing agent, and in addresses it can mean a US state.
If the abbreviation appears next to a rate or an amount, it almost always means per annum. Contracts sometimes spell out the day count, which is the number of days assumed in a year when interest is worked out.
Using 365 days instead of 360 gives a slightly lower daily charge, so it is worth checking which basis applies to a loan.
In practice
Real-world examples.
Example
A savings account offers 4% pa interest on a balance of $25,000. After one year with no withdrawals the interest is 25,000 x 0.04 = $1,000. The saver compares it with another account paying 3.9% pa but compounding monthly.
Example
A job advert offers a salary of $72,000 pa. The candidate divides it by 12 to get $6,000 a month before tax. She uses that figure to plan her monthly budget.
Example
A landlord charges rent of $18,000 pa on a shop, payable quarterly. Each quarterly instalment is 18,000 / 4 = $4,500. The tenant's finance team enters the amount as $18,000 pa in its lease schedule.
Formula
Calculation
Simple interest = principal x annual rate x time in years
Effective annual rate = (1 + nominal rate / number of periods) to the power of number of periods - 1
A business borrows $50,000 at 8% pa simple interest for 18 months. Time = 18 / 12 = 1.5 years. Interest = 50,000 x 0.08 x 1.5 = $6,000. For a different loan at 12% pa charged monthly, the monthly rate is 12% / 12 = 1%. Effective annual rate = (1.01 to the power of 12) - 1 = 1.1268 - 1 = 12.68%.
Reading the result: on a $10,000 loan, 12% pa charged monthly costs about $1,268 over the year in interest, not $1,200, a difference of $68. The pa label alone does not show this, which is why lenders are often required to state the effective rate as well.
To go the other way, a monthly rate of 1% is not equal to 12% pa once compounding is included. A saver putting $10,000 at 12% pa compounded monthly ends the year with 10,000 x 1.1268 = $11,268, which is $68 more than simple interest of $1,200 would give.Case study
Seen in the real world.
Tamarind Studios is an illustrative, fictional design company comparing two loans of $100,000. Lender A quotes 9% pa with interest charged once a year, while Lender B quotes 8.8% pa with interest charged monthly.
The finance manager calculated the effective rate for each. Lender A costs 9.00%, and Lender B costs (1 + 0.088 / 12) to the power of 12 - 1, which is about 9.16%. The lender with the lower headline rate was actually more expensive.
The company chose Lender A, saving about $160 a year on the loan in this illustrative case. The lesson is that pa tells you the period, not the full cost, so effective rates should always be compared.
Watch out
Common mistakes.
- Assuming that 12% pa charged monthly costs exactly 12% over the year, when compounding makes the true cost higher.
- Comparing a monthly rate with an annual one without converting them to the same basis.
- Reading PA as power of attorney or personal assistant when it appears next to an interest rate.
Questions
People also ask.
What does pa stand for?
It stands for per annum, a Latin phrase meaning each year.
Is pa the same as APR?
Not quite, since APR is a standardised annual cost measure that may include fees, while pa simply states a yearly rate.
How do I convert a pa rate to monthly?
For a simple estimate, divide the annual rate by 12, so 6% pa becomes 0.5% a month.
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