TVM - Interest Rates

effective annual rate (EAR)

• indicates the total amount of interest that will be earned at the end of one year

• considers the effect of compounding

  • AKA effective annual yield (EAY) or annual percentage yield (APY)

monthly interest rate

(1+ EAR) ^{(1 / compounding period)} - 1

effective rates

• C = FV / {(1/r) * [(1+r)ⁿ - 1]}

• =PMT(rate, nper, PV, FV)

annual percentage rate

• indicates the amount of simple interest earned in one year

• does not reflect the true amount earned over one year

• cannot be used as a discount rate

• not an EAR

simple interest

amount of interest earned without the effect of compounding

steps for APR

1. convert the APR to its implied effective rate, r, per compounding period

   • r = APR / k compounding periods per year

2. convert the implied effective interest rate per compounding period, r, into EAR

   • 1 + EAR = (1+r)^k

3. needed with the final desired rate is not an EAR or any other effective rate

   • to present the final rate with a different period of quotation:

     • multiply the effective rate per the final rate’s compounding period * the final rate’s compounding frequency

converting APR to EAR

1 + EAR = (1 + APR/k)^k

loan/mortgage payments

• payments are made at a set interval (monthly)

• each payment made includes the interest on the loan + some part of the loan balance

• all payments are equal and the loan is fully repaid with the final payment