Present Value Formula
Before knowing the present value formula, can you recall where you have heard this? The "present value" and "future value" are the terms related to compound interest.
 The "present value" or "PV" is the initial amount (the amount invested, the amount lent, the amount borrowed, etc).
 The "future value" or "FV" is the final amount. i.e., FV = PV + interest.
The term “present value” refers to the application of the time value of money that discounts the future cash flow to arrive at its presentday value. Let us understand the present value formula in detail in the following section.
What is the Present Value Formula?
Present value (PV) formula finds application finance to calculate the present day value of an amount that is received at a future date. The present value formula (PV formula) is derived from the compound interest formula. The compound interest formula is,
FV = PV (1 + r / n)^{n t}
Dividing both sides by (1 + r / n)^{n t},
PV = FV / (1 + r / n)^{n t}
Thus, the present value formula is:
PV = FV / (1 + r / n)^{n t}
Here,
 PV = Present value
 FV = Future value
 r = Rate of interest (percentage ÷ 100)
 n = Number of times the amount is compounding
 t = Time in years
The value of n varies depending on the number of times the amount is compounding.
 n = 1, if the amount is compounded yearly.
 n = 2, if the amount is compounded halfyearly.
 n = 4, if the amount is compounded quartyearly.
 n = 12, if the amount is compounded monthly.
 n = 52, if the amount is compounded weekly.
 n = 365, if the amount is compounded daily.
Let us have a look at a few solved examples to understand the present value formula better.

Example 1: Jonathan borrowed some amount from a bank at a rate of 7% per annum compounded annually. If he finished paying his loan by paying $6,500 at the end of 4 years, then what is the amount of loan that he had taken? Round your answer to the nearest thousands.
Solution:
To find: The present value (borrowed amount) of the given amount.
The future value is, FV = $6500.
The time is t = 4 years.
n = 1 (as the amount is compounded annually).
The rate of interest is, r = 7% =0.07.
Substitute all these values in the the present value formula:
PV = FV / (1 + r / n)^{n t}
PV = 6500 / (1 + 0.07/1)^{1(4)} = 6500 / (1.07)^{4} ≈ 5,000 (The answer is rounded to the nearest thousands).
Answer: The borrowed amount = $5,000.

Example 2: Mia invested some amount in a bank where her amount gets compounded daily at 5% annual interest. What is the amount invested by Mia if the amount she got after 10 years is $1,650? Round your answer to the nearest thousands.
Solution:
To find: The present value (invested amount) of the given amount.
The future value is, FV = $1650.
The time is, t = 10 years.
n = 365 (as the amount is compounded daily).
The rate of interest is, r = 5% =0.05.
Substitute all these values in the present value formula:
PV = FV / (1 + r / n)^{n t}
PV = 1650 / (1 + 0.05/365)^{365(10)} ≈ 1000 (The answer is rounded to the nearest thousands).
Answer: The invested amount = $1,000.