Annual percentage rate, or APR, and effective annual rate, usually abbreviated as EAR, are two ways of expressing the time value of money. They may be used to describe how much a loan will cost, or they may describe the annualized income from an investment. How APR and EAR are calculated depends on whether they are describing costs or income.

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When relating to the cost of a loan, APR focuses only on interest accrual over the loan term, while EAR also considers additional lending fees involved. When relating to annualized income from investments, APR focuses on interest paid at the frequency of accrual, but EAR also considers the investment's earnings considering the interest paid will be reinvested at the same interest rate.

## APR on Loans

In terms of loan interest, APR is an annualized figure representing how much a loan will cost per year, given how frequently interest is accrued and the term of the loan. The difference is important, because in most installment loans, early payments are primarily payments of interest, while final payments are primarily payments of the base amount of the loan itself. In addition, the more frequently interest is charged against the remaining loan, the more interest is paid.

APR takes into account all interest that will actually be paid against the loan and divides it by the term of the loan in years. So for a $100,000 loan, if actual interest over the course of 10 years is $150,000, the annualized interest cost of the loan would be $15,000. Since $15,000 is 15 percent of $100,000, the APR for this loan is 15 percent.

## EAR on Loans

EAR starts with the same figures as APR but also factors in any additional fees the lender may charge. This will give a more comprehensive expression of the cost of the loan.

In the case of 10-year, $100,000 loan with a 15 percent APR, a bank may charge a $30 annual loan fee. Thus the total interest cost plus total fees would come to $150,300. So the EAR on this loan would actually be 15.03 percent.

## APR and EAR in Investing

When expressing investment income, APR and EAR are calculated differently. In this case, APR is the interest paid on the investment times the frequency with which it is accrued. EAR, on the other hand, is an expression of how much the investment will earn assuming that the interest paid on it is reinvested at the same interest rate.

So if an investment pays 10 percent in interest compounded every six months, the APR is 20 percent. However, the EAR would be 21 percent, because at the end of the second six months, you would also be making 10 percent interest on the interest reinvested at the end of the first six months.

## Implications of the Differences

Differences between APR and EAR are most significant for loans that carry high closing costs and/or annual fees, such as mortgage loans. In this case, EAR will be much more useful in budgeting for the cost of borrowing the money. In investing, EARs are more important for investments in which interest cannot be withdrawn midway through the term of the loan. EAR will be more pertinent to an individual retirement account, for instance, than for an income investment in which money is paid to the investor rather than reinvested.

### References

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