Bank 1 lends funds at a nominal rate of 7% 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 interest rate will they charge their customers? Round your answer to three decimal places. Do not round intermediate calculations.

Bank 1 lends funds at a nominal rate of 7% 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 interest rate will they charge their customers? Round your answer to three decimal places. Do not round intermediate calculations.

 

answer:

6.939%

Step-1:
Calculate effective annual interest rate of Bank 1:
Effective annual interest rate
= ((1+(i/n))^n)-1 i = Nominal Rate
n = payment frequency
Effective annual rate of Bank 1:
= ((1+(.07/2))^2)-1 i = 7.00%
= 7.122% n =                 2
Step-2:
Now with the use of effective annual interets rate of Bank 1, Calculate nomina lInterest rate of Bank 2:
Effective annual rate of Bank 2:
7.122% = ((1+(i/4))^4)-1 i = ?
                     1.07122 = ((1+(i/4))^4) n =                 4
1.07122^(1/4) = (1+(i/4))
                  1.017348 = (1+(i/4))
                  0.017348 = i/4
i = 6.939%
Thus, Bank 2 will charge their customer at Nominal interest rate of 6.939%
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