Question

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EAR versus APR Two banks in the area offer 30-year, $200,000 mortgages at 5.3 percent and charge a $2,400 loan application fee. However, the application fee charged by Insecurity Bank and Trust is refundable if the loan application is denied, whereas that charged by I. M. Greedy and Sons Mortgage Bank is not. The current disclosure law requires that any fees that will be refunded if the applicant is rejected be included in calculating the APR, but this is not required with nonrefundable fees (presumably because refundable fees are part of the loan rather than a fee). What are the EARs on these two loans? What are the APRs?

Answer 1

Effective Annual Rate (EAR) is the interest rate which expressed as if it were compounded once per year. In other words it is the rate of interest rate which an investor gets in a particular year after accounting for the compounding effects. If an interest rate is given as 12 percent, compounded daily it is the effective annual rate.

The nominal is the rate of interest which is declared in a contract. The nominal annual interest rate is also called the annual percentage rate, or APR. Effective Annual Rate (EAR) is the rate of interest rate which an investor gets in a particular year after accounting for the compounding effects. So APR is the yearly return while EAR is the yearly yield after compounding. EAR is calculated as follows:

Where:

Annual percentage rate is defined as APR

Compounding period is defined as M

Effective annual rate is defined as EAR

or Present value of annuity is the today’s value of expected future cash flow of equal payments. Suppose, if an investor wants to know the present value of future payment series, he can use the present value of an ordinary annuity. It will be calculated as follows:

Where:

Present value of an ordinary annuity is defined as PVA

Payment amount is defined as PMT

Interest rate is defined as i

Number of period is defined as n.

Compounding in a year is defined as m

Here first requirement is to calculate the APR and EAR of the loan along with the refundable fee. The application fee is $2,400. So the borrowing amount would be $202,400 to have $200,000 in hand after deducting the fee.

Now by using the PVA equation, calculate the payment:

The above calculated amount can be used to find the rate with the actual borrowed amount:

By hit and trial, r is coming out to be.

Here calculate the APR:

Therefore, the APR is.

And calculate the EAR:

Therefore, the EAR is.

If the fee is non-refundable then in that case APR will be same as quoted that is. While the EAR will be calculated as follows:

Therefore, the EAR is.