Annual Percentage Rate (APR) is usually used for loans, mortgages, and so on. APR represents an annualized expression of the cost of borrowing money.
When you take out a loan or mortgage on a property, in addition to the interest, you are required to pay some other transaction costs such as points*, loan origination fees, a home inspection fee, mortgage insurance premiums, … . Considering these costs, the amount of money that you will receive is actually somewhat less than what you requested. APR is the expression that reflects some of these costs, and under the Federal Truth in Lending Law, Regulation Z, the lender is required to provide this information to the borrower. Since APR includes mentioned transaction costs, it is higher than interest rates. You can think of APR as the rate of return on the loan taking process considering its costs.
* Loan points are a percentage of the loan value that is deducted as transaction cost.
APR can be a good tool for comparing different loans offered by lenders. But there are two issues that need to be considered before comparing APRs:
 how the lender calculates APR and what costs are included;
 the fact that the difference between APR and loan interest rate is higher for smaller loans with shorter lifetimes, considering similar costs.
For More information about APR please watch the video linked below.
Annual Percentage Rate Video (1:34)
Investopedia presents: Annual Percentage Rate
The annual percentage rate or APR is the cost per year of borrowing. By law, all financial institutions must show customers the APR of a loan or credit card. Which clearly indicates the real cost of the loan. APR is not the same as the interest rate on a loan. Loans charge and interest rate but usually also charge other fees such as closing costs, origination fees, or insurance costs which are typically wrapped into the loan. If two loans have the same interest rate but one has much higher fees than the other, simply shopping by interest rates won’t give an accurate comparison of the loan's true cost. That’s why there is an APR. By factoring in other fees APR gives a more accurate estimate of the cost per year of a loan. For this reason, the APR is generally higher than the interest rate.
For example, a mortgage company may offer a customer an interest rate of 4% on a mortgage loan of $100,000 but after closing costs and other fees, the loan may have an APR of 4.1%. Unfortunately, not all financial institutions include the same fees in their APR calculation, so APRs are not always a perfect comparison tool. When comparing load or credit card APR’s ask what fees are included so your comparison is accurate.
Example 31
Calculate the APR for a 5year, $25,000 loan with the interest rate of 6% (compounded annually), considering 1.5 points and loan originating fee of 250 dollars. Assume all the costs are deducted at the time of taking the loan (present time).
Note: 1.5 points equals a cost of 1.5% of the loan value.
First, the uniform series of annual payments needs to be calculated.
Regarding Table 112 and Equation 16
$$\begin{array}{l}A=P*A/{P}_{i,n}=P\left[i{\left(1+i\right)}^{n}\right]/\left[{\left(1+i\right)}^{n}1\right]\\ A=25,000*A/{P}_{6\%,5}=25,000*\left[0.06{\left(1+0.06\right)}^{5}/\left[{\left(1+0.06\right)}^{5}1\right]\right]\\ A=5,934.91\text{dollarsperyear}\end{array}$$Then, we have to calculate the costs and deduct them from the loan:
$$\begin{array}{l}\text{1.5points}=1.5\%*\text{}25,000=\text{\$}375\\ \text{Loanoriginationfee}=\text{\$}250\text{}\\ \text{Costofloan}=375+250=\text{\$}625\text{}\end{array}$$So, borrower will receive $24,375 at the present time and pay $5,934.91 to the bank, each year, starting from end of the year 1:
Now, we have to calculate the rate of return for such a project.
Loancost= 24,375  A=5,934.91  A=5,934.91  A=5,934.91  A=5,934.91  A=5,934.91 


0  1  2  3  4  5 
Present value of loan – present value of the costs = present value of all annual payments
$$\begin{array}{l}25,000\u2013625=5,934.91*\left(P{/}_{Ai,5}\right)\\ 24,375=5,934.91*\left[{\left(1+i\right)}^{5}1/\left[i{\left(1+i\right)}^{5}\right]\right]\end{array}$$With the trial and error technique, explained in the Lesson 2 section “BreakEven and Rate of Return (ROR) Calculations II,” we can calculate i =6.94% as the APR for loan.
Please watch the following video, Calculating APR for a loan or mortgage (4:43).
Excel formula to calculate Rate of Return
Rate of return for an investment can be determined by the try and error method that is previously explained. Also, a convenient way to learn to calculate rate of return is to use Microsoft Excel or Google Sheets and apply Internal a Rate of Return (IRR) function to the cash flow.
Note: You have to enter the occurred amounts in the spreadsheet in the form of cash flow (you can enter the years in horizontal or vertical direction). It means inflow and outflow of cash should be entered with different signs (depending on the project). So, you can enter the loan with negative signs at the present time and annual payments in following years with positive signs.
More information about the IRR function in provided in following links.
IRR Function in Microsoft Excel
Please watch the following video, Internal Rate of Return (1:58).
Figure 31 displays the APR calculations for Example 31.