Future Value and Compounding
Future value is the value of your current position (asset/liability) at a later point in time. It’s a summation of ‘Value of Current Position’ Pv and accumulated interest I over time n.
So, Future Value (Fv) = Present value (Pv) + Accumulated Interest (In)
Accumulated interest can be either simple interest or compound interest.
Simple Interest – Interest is accrued on the initial principle amount only, year on year. So for principle value of Pv, interest rate of I% and time period of n
Simple Interest = (Pv * I% * n)
So Future Value = Pv + (Pv * I% * n)
Future Value = Pv (1 + n*I%) …………………………………… (i)
Compound Interest – Here interest is calculated on the starting principle amount as well as accumulated interest over the years. The point at which interest amount is added to the total amount depends on the frequency of compounding which can be say, yearly, quarterly, monthly or even continuous
So, at end of year one, value = Pv + Pv*I% = Pv*(1+I%)
At end of year two, value = Pv*(1+I%) + Pv*(1+I%)*I% = Pv*(1+I%)*(1+I%) = Pv*(1+I%)^2
And so on, to year n – Future Value at yearly compounding
Fv= Pv*(1+i%)^n ………………………………………………………… (ii)
Generalizing to c compounding per year, Fv = Pv *(1+i/c%)^(n/c), I = annual interest rate
Present Value and discounting
This is quite the reverse of the above topic.
Present value is the current worth of any asset/liability based on fair market value.
Discounting is the process of arriving at the present value of an asset/liability from a future value based on applicable discount rate.
From (ii) above it follows that
Pv = Fv / (1+i)^n
in 400 words answer the following: 1. Please choose two topics of your choice from chapters...
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