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EXAMPLE 2-A.2

The Premier Rank 1 offers to 10 percent interest on a deposit of one year. Assuming (i) annual, (ii) half-yearly and (iii) quarterly frequency of interest compute the effective rates of interests in the three alternatives.

Solution  Assuming a deposit of Rs 1.000. the computation of the effective rates of interest is shown below.

We can determine the effective rate given the nominal rate and vice-versa. Denoting the nominal rate of interest compounded/convertible PTHLY (where P represents the frequency of payments during the year such as 12 for monthly payment. 4 for quarterly payment and two for half-yearly payment) as i” and the corresponding effective rate of interest as i, symbolically

EXAMPLE 2-A.3

Assuming [a) i = 0.0125 and (b) i” = 0.1025,  find the values of  (1)  i” and (2) i12”.

Solution

Similar to the relationship between the nominal and effective rates of interest, the mathematical relationship between effective and nominal rates of discount is given by Equations 2.A.4 and 2-A.5. The nominal rates or interest and discount rate employed in computing the present value or annuities payable P-thly.

EXAMPLE 2-A.4

Assuming d12 =  0.12 and (i)2 = 0.12 find the value of (a) d and (b) d”

Solution

The relationship between various nominal and effective rates of interest and discount is given in Table A.5