Question

Gomez Electronics needs to arrange financing for its expansion program. bank a offers to lend Gomez the required fund on a loan where interest must be paid monthly, and the quotes rate is 8 per cent. bank b will charge 9 percent, with interest due at the end of the year, what is the difference in the effective annual rates charged by the two banks?

Answer 1

Answer : Difference is 0.7%

Calculation of Effective Annual Rate :

Effective Annual rate = [(1 + r)^n - 1 ]

where r is the rate of interest per period

n is the number of compounding period

Effective annual rate when compounded monthly :

Effective Annual rate = [(1 + 0.006667)^12 - 1 ]

= [1.083 - 1]

= 0.083 or 8.3%

where r is the rate of interest per period i.e 0.08 / 12 = 0.0066667

n is the number of compounding period i.e 12

Effective annual rate when compounded annually :

Effective Annual rate = [(1 + 0.09)^1 - 1 ]

= [1.09 - 1]

= 0.09 or 9%

where r is the rate of interest per period i.e 0.09

n is the number of compounding period i.e 1

Difference in the effective annual rates charged by the two banks = 9% - 8.3% = 0.7%