# Formulas used to determine the valuation

#### archdevil

##### Royal Member
Amount of ₹ 1.00
To find the amount that will accumulate at the end of N years if re 1.00 is invested today at the rate of interest of i % per annum

Amount of ₹ 1.00 = (1+ i )n

Where i is the rate of interest viz. 0.03 for 3 %, 0.05 for 5 % etc and n is the No of the years

Present value of ₹ 1.00
To find the present value of ₹ 1.00 payable at the n years at the rate of interest of i percent/annum

Present value of ₹ 1.00 = 1/ (1+ i )n

Where n is the no of years and I is the rate of rate of interest viz. 0.03 for 3 % rate of interest

Amount of ₹ 1.00 per annum
To find the amount that will accumulate at the end of n years if re. 1.00 is invested at the end of every year at the rate of interest of 1 percent per annum.

Amount of ₹ 1.00 per annum = (1+ i )n - 1

Where n is the number of years and i is the rate of interest viz. 0.03 for 3% rate of interest.

Annual sinking fund
To find the amount should be invested every year at the rate of interest of i percent per annum so that it will accumulate to re 1.00 at the end of n years.

Annual sinking fund = i/(1+ i )n – 1

Where i is the rate of interest viz. 0.03 or 3%, and n is the no. of years.

Present value of ₹ 1.00 per annum (single rate). (this is also called as the year’s purchase (single rate) for n years).
To find the present value of the total accumulation at the end of n years if re 1.00 is proposed to be invested at the end of every year at the rate of interest of i percent per annum.

Here, i.e. in single rate calculations, it is assumed that the invested capital (present value) can be redeemed by paying in to sinking fund an annual amount which will accumulate at compound interest at the percent at which the annual payment of re 1.00 will be invested.

Present value of ₹ 1.00 per annum (single rate) (i.e. year’s purchase(single rate) for n years).

[1 – 1/(1+ i )n ]

Where i is the rate of interest per annum viz. 0.03 for 3% and n is the no. of year

Present value of ₹ 1.00 per annum (Dual Rate)
To find the present value of the total accumulate at the end of n years if re 1.00 is proposed to be invested at the end of every year at the rate of interest of i per annum and where allowance is to be made foe invested capital (i.e. the present value) to be redeemed at the end of n years by paying in to an annual sinking fund at a different rate percent, usually much lower than i.

Present value of ₹ 1.00 per annum (dual rate) (i.e. year’s purchase (dual rate) for n years).

1 – V/i – (V x d)

Where V = Present value of re 1.00 received at the end of n years at the rate percent at which an annual sinking fund can be invested.

d = Difference between interest on re 1.00 for year at the two given rates per cent.

i = the rate of interest on the yearly investments that is to be allowed.