Answer to Question #168150 in Finance for Andi

Question

This is a question about interest rates. How do I know when to use a period rate rather than an effective annual rate.

Question: A perpetuity pays 40$ per year to infinity.Considering a required rate of return of 10% APR, compounded semi-annually, what is the present value of thr perpetuity. To compute the anwser the apr is converted to EAR.

In which situations would we convert it to a periodic rate. Or do we always convert the APR to an EAR?

Answer 1

The periodic interest rate is the interest rate accrued on a loan or realized on an investment over a certain period of time. Typically, lenders quote interest rates on an annual basis, but in most cases, interest is aggregated more often than annually. As a result, the periodic interest rate is the annual interest rate divided by the number of mixing periods.

When discussing loans or investments, the annual interest rate quoted is usually the nominal interest rate, and the effective interest rate is the actual interest rate after the impact of compounding has been taken into account.

This is a perpetual annuity.

APR is converted to EAR.

$EAR=(1+r)^n-1=(1+\frac{0.1}{2})^2-1=0.1025$

$PV=\frac{A}{i}=\frac{40}{0.1025}=390.24$

APR is commonly used to standardize borrowing or savings rates so that they can be compared on an equal footing. You'll always see loans and credit cards disclosing their APRs in their advertising and their loan agreements. However, lenders can manipulate APRs somewhat by choosing which fees to include when they calculate their rates.

When you deposit money into a savings account, money market account or certificate of deposit, you'll frequently see EAR quoted. The reason is simple enough – EAR is larger than APR and thus more enticing to savers. EAR is also more correct because it recognizes the action of compounding to grow your money faster.