Per Annum

What Does Per Annum Mean?

Per annum (abbreviated as p.a.) is a Latin phrase meaning “per year” or “annually”. It is a financial term used to describe the frequency of interest payments, income, or expenses that occur in a year. Per annum is commonly used in finance and business to calculate annual rates, yields, returns, and salaries. Understanding the concept of per annum is crucial in financial planning, budgeting, and investment decisions.

Types of Per Annum

Simple Interest per Annum

Simple interest per annum is the interest earned on a principal amount for a year, calculated as a percentage of the principal. Simple interest per annum is commonly used in short-term loans and investments, where the interest rate is fixed, and the interest is paid in full at the end of the term. The formula to calculate simple interest per annum is:

Simple Interest per Annum = (Principal × Interest Rate × Time)/100

Compound Interest per Annum

Compound interest per annum is the interest earned on a principal amount, which is reinvested at the end of each compounding period for a year, calculated as a percentage of the principal. Compound interest per annum is commonly used in long-term loans and investments, where the interest rate is variable and the interest is paid periodically. The formula to calculate compound interest per annum is:

Compound Interest per Annum = Principal × (1 + Interest Rate/n)^(n × Time) – Principal

Where n is the number of compounding periods per year.

Nominal Annual Interest Rate

The nominal annual interest rate (also called the stated annual interest rate) is the yearly interest rate stated in a loan or investment agreement. The nominal annual interest rate does not take into account the effect of compounding, fees, or other factors that affect the actual yield or return. The nominal annual interest rate is commonly used in advertising and marketing to attract customers to loans and investments.

Effective Annual Interest Rate

The effective annual interest rate (also called the annual percentage yield or APY) is the yearly interest rate that takes into account the effect of compounding, fees, and other factors that affect the actual yield or return. The effective annual interest rate represents a loan or investment’s true cost or benefits over a year. The formula to calculate the effective annual interest rate is:

Effective Annual Interest Rate = (1 + Nominal Annual Interest Rate/n)^n – 1

Where n is the number of compounding periods per year.

Per Annum Usage in Different Fields

Finance

In finance, per annum is used to express the annual interest rates, yields, and returns of loans, investments, and savings. For example, a mortgage with a nominal annual interest rate of 5% per annum means that the borrower will pay 5% of the principal amount in interest per year. A savings account with a compound interest rate of 4% per annum means the account will earn 4% interest on the principal amount, which is reinvested at the end of each compounding period over a year.

Salary

In salary negotiations and employment contracts, per annum is used to express an employee’s annual salary. For example, a job offer with a salary of $50,000 per annum means that the employee will earn $50,000 in total over a year, paid in equal installments, such as monthly or bi-weekly.

Budgeting

In budgeting, per annum is used to estimate an individual or organization’s annual income and expenses. For example, a household budget with an estimated income of $80,000 per annum and estimated expenses of $70,000 per annum means that the household expects to earn $80,000 in total and spend $70,000 in total over a year, resulting in a surplus or deficit of $10,000 per annum.

Investment

In investment, per annum is used to calculate the returns and risks of different investments over a year. For example, an investment portfolio with an average annual return of 8% per annum means that the portfolio is expected to earn 8% of the total value of the portfolio in returns over a year. The annual returns of different investments can be compared using the effective annual interest rate to take into account the effect of compounding, fees, and other factors.

Per Annum vs. Per Annum Cumulative

Per annum and per annum cumulative are two different ways of expressing the frequency and amount of interest payments or returns over a year. Per annum refers to the simple or compound interest or returns earned in a year, whereas per annum cumulative refers to the cumulative interest or returns made over multiple years. For example, if a loan has an interest rate of 5% per annum and a term of three years, the total interest paid will be 15% per annum cumulative.

Per Annum Cumulative Formula

The formula to calculate per annum cumulative interest or returns is:

Per Annum Cumulative = (1 + Per Annum Interest or Returns)^Number of Years – 1

For example, if an investment has an average annual return of 8% per annum over five years, the per annum cumulative return will be:

Per Annum Cumulative = (1 + 8%)^5 – 1 = 46.93%

Per Annum in Accounting

In accounting, per annum is used to calculate the annual depreciation expense of fixed assets. Depreciation is the process of allocating the cost of a fixed asset over its useful life. The depreciation expense per annum is calculated based on the cost of the asset, its useful life, and the depreciation method used. The formula to calculate the depreciation expense per annum using the straight-line method is:

Depreciation Expense per Annum = (Cost of Asset – Salvage Value)/Useful Life

For example, if a company purchases a machine for $10,000 with a useful life of five years and a salvage value of $2,000, the depreciation expense per annum using the straight-line method will be:

Depreciation Expense per Annum = ($10,000 – $2,000)/5 = $1,600 per annum

Conclusion

Per annum is a financial term used to express the frequency and amount of interest payments, income, or expenses that occur in a year. Per annum is commonly used in finance, business, accounting, and personal finance to calculate annual rates, yields, returns, salaries, and depreciation expenses. Understanding the concept of per annum is essential in making informed financial decisions and planning for the future.