Present Value of Quarterly Payment

To calculate the present value of quarterly payments of Rs 100 for 10 years at an annual interest rate of 18%, we can use the formula for the present value of an annuity. The formula is:

PV = PMT x [1 - (1 + r/n)^(-nt)] / (r/n)

Where PV is the present value of the annuity, PMT is the payment per period, r is the annual interest rate, n is the number of compounding periods per year, and t is the number of years.

Plugging in the values, we get:

PV = 100 x [1 - (1 + 0.18/4)^(-4x10)] / (0.18/4)
PV = Rs 1,454.54

Therefore, the present value of quarterly payments of Rs 100 for 10 years at an annual interest rate of 18% is Rs 1,454.54.

Present Value of Annuity Compounded Semi-Annually

To calculate the present value of an annuity of Rs 100 per quarter for 4 years, if the interest is compounded semi-annually at a nominal rate of 6%, we can use the formula for the present value of an annuity again. However, since the interest is compounded semi-annually, we need to adjust the variables in the formula accordingly.

The formula is:

PV = PMT x [1 - (1 + r/n)^(-nt)] / (r/n)

Where PV is the present value of the annuity, PMT is the payment per period, r is the nominal interest rate, n is the number of compounding periods per year, and t is the number of years.

Plugging in the values, we get:

PV = 100 x [1 - (1 + 0.06/2)^(-2x4)] / (0.06/2)
PV = Rs 369.79

Therefore, the present value of an annuity of Rs 100 per quarter for 4 years, if the interest is compounded semi-annually at a nominal rate of 6%, is Rs 369.79.

Explanation

The two problems use the formula for the present value of an annuity, which is a financial concept that calculates the current value of a stream of equal payments made at regular intervals over a set period of time. In the first problem, we are given the payment amount, the interest rate, and the time period, and we use the formula to calculate the present value. In the second problem, we are given the payment amount, the nominal interest rate, the compounding period, and the time period, and we adjust the variables in the formula accordingly to calculate the present value.