High School

1. Vijay has invested a sum of money at an interest rate of 4% per annum compounded quarterly for a period of 5 years. As discussed in the class, what are the values of the following variables: j: _0.04_ m: 12x5=60 i: j/m=_0.04/60_= 0.0006_ n: 5x4=20 Calculate the effective interest rate f: (1+i)^m -1

Answer :

The effective interest rate for Vijay's investment over the 5-year period is approximately equal to 0.0369 or 3.69%.

In this scenario, we have the following variables:

j represents the annual interest rate, which is 4% (0.04 in decimal form).

m represents the number of compounding periods per year, which is 12 (as interest is compounded quarterly).

i represents the periodic interest rate, which is calculated by dividing the annual interest rate by the number of compounding periods per year. In this case, i is equal to 0.04 divided by 60, resulting in 0.0006.

n represents the total number of compounding periods over the investment period, which is 5 years multiplied by 4 (since interest is compounded quarterly), giving us a value of 20.

To calculate the effective interest rate, we use the formula f = (1 + i)^m - 1. Plugging in the values, we have f = (1 + 0.0006)^60 - 1. Evaluating this expression gives us the effective interest rate over the 5-year period.

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