Investment Analysis with Different Compounding Frequencies

In this problem, Minakshi invests eighty-five thousand rupees at an eight percent annual interest rate for one year. We need to calculate the interest earned for three different compounding frequencies: yearly, every six months, and every three months.

Let's list our known values. The principal P is eighty-five thousand rupees, the annual interest rate r is eight percent, and the time t is one year.

The general formula for the amount after compound interest is A equals P times one plus r over n, all to the power of n times t. Here, n is the number of times interest is compounded per year.

For part one, interest is compounded yearly. This means n equals one.

Plugging in our values, the amount equals eighty-five thousand times one plus zero point zero eight over one, to the power of one.

This simplifies to eighty-five thousand times one point zero eight, which equals ninety-one thousand eight hundred rupees.

Subtracting the principal, we find the interest received is six thousand eight hundred rupees.

Now for part two: interest compounded every six months. This is semi-annual compounding, so n equals two.

Dividing the rate by two gives four percent, or zero point zero four, per period.