# APR

The APR (Annual Percentage Rate) is a simple nominal interest rate representing annual interest accrued.  APR is the base rate that allows linear compounding period after period.

Periodic Rate = APR / n

When n = Frequency of compounding within a year.

APR is used in the context of costs: i.e. Inflation rate, interest rate on debt.

If the frequency of compounding is annual, then APR will be the same as the APY.

## Putting Annual Percentage Rate (APR) in Context

Consider the financing of a commercial office building acquisition. The property, valued at \$10 million, is located in a thriving business district and comprises 100,000 square feet of rentable space. The buyer, an investment group, decides to finance 80% of the purchase price (\$8 million) through a commercial mortgage. The bank offers them a loan with an APR of 5%.

In this scenario, the APR effectively represents the cost of borrowing the funds on an annual basis, excluding other possible fees like closing costs or loan origination fees. The simplicity of APR allows the investors to compare this loan to other financing options quickly.

• Loan Amount: \$8,000,000
• APR: 5%
• Annual Interest Expense: APR x Loan Amount = 0.05 x \$8,000,000 = \$400,000

Thus, each year, the investment group will incur \$400,000 in interest expenses alone, assuming the loan interest is calculated without further compounding within the year (as APR assumes linear, or simple, interest).

This example helps demonstrate the straightforward application of APR in evaluating the direct financial impact of loan terms in commercial real estate transactions, aiding in transparent and efficient decision-making for investors.

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