PRESENT VALUE: This present value of Rs A due n years later is the amount of money needed now so that if it is invested now at a certain rate of interest, the sum of Rs. A can be obtained at the end of n years.
Thus, when we sy that Rs. P is the present value of Rs. A due n years later at the compound rate’ of interest R% per annum, it means that if we invest Rs. P now for n rears at R% per annum compounded annually, we will get Rs. A at the end of n years. i.e. A = Amount of Rs. P after n years at the rate of R% per annum compounded
Find the present value of Rs. 1210 due 2 years hence at 10% per annum compounded annually.
SOLUTION We have,
A = Rs. 1210, n = 2 years and R = 10% per annum
This means that if we invest Rs. 100(1 for 2 years at 10% per annum compounded annually, then after 2 years, we will obtain Rs. 1210.
REMARK If the interest is R% per annum compounded half-yearly, then the present value of Rs. A payable after n years is given by
Similarly, the present value of Rs. A due n years later at R% per annum compounded quarterly is given by
\( P= A(1+R/400)^-^4^n \)