Question

Bank 1 lends funds at a nominal rate of 8% with payments to be made semiannually. Bank 2 requires payments to be made quarterly. If Bank 2 would like to charge the same effective annual rate as Bank 1, what nominal annual rate will they charge their customers? Round your answer to three decimal places. Do not round intermediate calculations.

Answer 1

Answer: 7.922%

Explanation:

Bank 1 lends at nominal rate of 8% and payments made is semiannually,

So,

Semiannual rate of bank 1 = 4%

Effective annual rate of Bank 1:

$EAR=(1+half\ yearly\ rate)^{2}-1$

$EAR=(1+0.04)^{2}-1$

= 8.16%

If Bank 2 wants to maintain the same level of EAR at quarterly compounding:

$(1+quarterly\ rate)^{4} =EAR+1$

$(1+quarterly\ rate)^{4} =8.16\ percent+1$

$(1+quarterly\ rate)^{4} =1.0816$

$(1+quarterly\ rate) =(1.0816)^{\frac{1}{4} }$

$(1+quarterly\ rate) =1.01980390271$

Quarterly rate = 1.01980390271 - 1

                       = 1.980390%

Nominal annual rate for Bank 2 = Quarterly rate × 4

                                                       = 1.980390% × 4

                                                       = 7.9215% or 7.922%