Calculation of Present Value of Investment

Given:


Interest rate = 6% (Compounded semiannually)


Time period = 6 years


Amount received = Rs. 9000

Formula:


Present Value = Future Value / (1 + r/n)^(n*t)


where


r = rate of interest (per annum)


n = number of times interest is compounded in a year


t = time period (in years)

Calculation:


r = 6% (Compounded semiannually)


n = 2 (Compounded semiannually)


t = 6 years


Future Value = Rs. 9000

Present Value = 9000 / (1 + 0.06/2)^(2*6)


Present Value = Rs. 6216.78

Therefore, the present value of investment is Rs. 6216.78.

Explanation:


The problem involves calculating the present value of an investment. In order to do so, we need to use the formula for present value of a future sum of money. This formula takes into account the interest rate, the number of times interest is compounded in a year and the time period for which the investment is made.

In this problem, the interest rate is 6% and interest is compounded semiannually (i.e. twice a year). The time period for the investment is 6 years and the amount received at the end of the time period is Rs. 9000.

Using the formula, we can calculate the present value of the investment to be Rs. 6216.78. This means that if the person invests Rs. 6216.78 now, at an interest rate of 6% compounded semiannually for 6 years, they will receive Rs. 9000 at the end of the time period.

Therefore, the present value of the investment is the amount of money that needs to be invested now in order to receive the future sum of Rs. 9000.

Present value P = A/(1+i)^n
As interest is compounded semi annually,
i = 6/200 = 0.03
n = 2×6=12
P = 9000/(1.03)¹² = Rs 6312.42