Question

First National Bank charges 13.7 percent compounded monthly on its business loans. First United Bank charges 14 percent compounded semiannually. Calculate the EAR for First National Bank and First United Bank.

Answer 1

Answer:

First National Bank    = 14.6%

First United Bank.=   = 14.8%

Explanation:

Effective annual rate is the equivalent annual rate o where interest rate is compounded at an interval shorter than a year.

It can be calculated as follows:

EAR = ( (1+r)^(n) -1) × 100

r -interest rate per period

n- number of period

EAR - Effective annual rate

First National Bank

r - interest rate per month = 13.7%/12 = 1.141%

number of period = 12 months

EAR =( (1+011141)^(12) - 1) × 100

       =  0.145938395 × 100

       = 14.59

      = 14.6%

First United Bank.

r- interest rate per quarter - 14%/4 = 3.5% per quarter

n- number of quarters = 4

EAR = ((1+0.035)^(4)- 1) × 100

      = 0.147523001 × 100

      = 14.8%