1. Find the effective annual rate (EAR) in each of the following cases: Stated R

Question

1. Find the effective annual rate (EAR) in each of the following cases:

Stated Rate (APR) Number of Times Compounded        Effective Rate (EAR)

          12%                                              Quarterly                                             

            8                                                  Monthly                                                

            7                                                  Daily                                                                     

          16                                                 Continuous   

b) Calculating Annuity Present Value. An investment offers $6700per year for 15 years, with the first payment occurring one year from now. If the required return is 8 percent, what is the value of the investment? What would the value be if payments occurred for 40 years? For 75 years? Forever?

Explanation / Answer

Effective annual rate = [1+(r/n)]n - 1

r- Annual Interest Rate
n - No. of compunding period

b) Annuity Present Value = Payment per period x [1-(1+r)-n ]/r
Payment per period = $6700

i) APV (n=15 years) = $57348.5

ii) APV (n= 40 years) = $79894.9

iii) APV (n=infinite years) = $83750

APR No. of times compunded EAR 12% (r=0.12) Quarterly (n=4) 12.5% 8% (r=0.08) Monthly (n=12) 8.3% 7% (r=0.07) Daily (n=365) 7.25% 16% (r=0.16) Continously (Formula:er -1) 17.4%

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