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7 February, 03:00

For an interest rate of 12% per year compounded continuously, find (a) the nominal rate per year, (b) the nominal rate per quarter; (c) the effective rate per quarter, and (d) the effective rate per month. For an interest rate of 12% per year compounded continuously, find (a) the nominal rate per year, (b) the nominal rate per quarter; (c) the effective rate per quarter, and (d) the effective rate per month.

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  1. 7 February, 03:52
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    a. 12% per annum

    b. 12% per annum

    c. 12.55% per quarter

    d. 12.68% per month

    Explanation:

    a. The nominal Rate is the base rate per compounding which in this case is 12% which is the base rate charged.

    b. the nominal rate per quarter is 12 % because nominal interest rate is the base interest rate which means it is the given rate used as reference to calculate other rats.

    c. The effective interest rate is calculated as follows by using the formula"

    ieffective = (1 + inom/n) ^n - 1

    where ieffective is the effective interest rate we are looking for per quarter.

    inom is the nominal interest rate given which is 12%.

    n is the number of periods per compounding so in this case 4 which is quarterly therefore we substitute the values to the formula above.

    i effective = (1+12%/4) ^4 - 1 the we compute

    i effective = 0.1255 x 100 then we multiply by 100 to convert to percentage.

    therefore ieffective = 12.55% per quarter.

    d. we calculate the effective interest rate per month using the above mentioned formula for effective interest rate:

    ieffective = (1 + inom/n) ^n - 1

    ieffective = (1 + 12%/12) ^12 - 1 we compute with a calculator

    ieffective = 0.1268 then we multiply by 100.

    ieffective = 12.68% compounded monthly
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