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# What is the present value?

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,