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5 January, 13:03

Bank A offers to lend you $100,000 at a nominal rate of 6%, compounded monthly. The loan (principal plus interest) must be repaid at the end of the year. Bank B also offers to lend you the $100,000, but it will charge 6.40%, with interest due at the end of the year. What is the difference in the effective annual rates charged by the two banks

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  1. 5 January, 13:30
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    0.30 % is the correct option

    Explanation:

    According to the given information,

    Nominal return for Riverside = 6.5%

    Nominal return for Midwest = 7.0%

    Periods for Riverside = 12

    Periods for Midwest = 1

    This problem can be worked using the conversion formula. The formula is shown below:

    Effective interest rate (Riverside) = {[1 + (rnom / N) ]^N} - 1

    = {[ 1 + (0.065 / 12) ]^ 12} - 1)

    = {[ 1 + 0.00542] ^ 12} - 1

    = 1.0670 - 1

    = 0.067 or 6.7%

    Therefore, the effective interest rate is 6.7% for Riverside

    But the effective interest rate for Mid west is 7.0%

    The difference is (7.0% - 6.7%) = 0.3%

    Therefore, the correct option is d) 0.30%
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