Present value(PV) of a given sum due at the end of a given period is that sum which together with its interest of the given period equals to the given sum.
Or in other words “PV describes how much a future sum of money is worth today”.
Let the objective is to have an amount A after
nyears from today. If the interest rate is ‘i’, then the amount is required to deposited now
so as to achieve the set target is-
Which is called the PV of A.
Note-
1. Sum due = PV + Interest on present value
Present value (Continuous compounding)-
We use the following formula if there is continuous compounding-
Where-
P = principal amount
A = Amount at future point of time
t = time
r = rate of interest
Example: Find out the present value of Rs. 1000 due in 2 years at 5% per annum compound interest, If the interest is paid yearly.
Sol.
Here, A = 1000, n = 2, i = 0.05
We have to find P-
By the formula-
Therefore the PV is Rs.907.03.
Example: Find the PV of Rs. 4,500 due after 3 years from now. the interest is compounded continuously at the interest rate of 6%.
Sol.
Here we have- A = 4500, t = 3, r = 0.06,
To find P,
