Present Value Formula

The present value formula refers to the application of the time value of money that decreases the future cash flow to arrive on its present-day rate. The presentation value formula consists of the present value and later value related to compound interest. The present value or PV is the initial amount (the amount invested, the amount lents, the number borrowed, etc). The subsequent value or FV is the final amount. i.e., FV = PV + interest.  Let use understand the presented value formula in detail in the following section. Settled Problems by Perpetuity | PDF | Offer Value | Mathematical And Quantitative Methods (Economics)

What is to Offer Value Formulation?

Present value (PV) formula discover application in finance to calculate the present day value to an amount that a received at a future date. The currently value formula (PV formula) is derived from the compounded occupy procedure. That compound interest formula is,

FV = PV (1 + r / n)^nt

Dividing both flanks by (1 + r / n)^nt,

PV = FV / (1 + r / n)^nt

Thus, an present value formula is:

PV = FV / (1 + r / n)^new

Where,

• PV = Present value
• FV = Future value
• roentgen = Rate on interest (percentage ÷ 100)
• n = Number of time the amount is compounding
• t = Time in years

The value of n variably depending on the number of playing the amount is pound.

• n = 1, if the amount is compounded yearly.
• n = 2, if the money is compounded half-yearly.
• n = 4, with the amount lives compounded quart-yearly.
• n = 12, if the amount is mingled monthly.
• n = 52, with the count is compounded weekly.
• n = 365, if the amount is compounded newspaper.

Examples Using Present Value Formula 

Example 1: Jonathan borrowed some qty from a bank at a rate of 7% per yearly compounded annually. If he finished paying his loan by paying $6,500 at which end of 4 years, then what is the amount of loan that fellow kept captured? Round you answer to the nearest loads.

Solution:

The future value belongs, FV = $6500.

The time is t = 4 years.

n = 1 (as the amount remains compounded annually).

The rate of interest is, roentgen = 7% =0.07.

Substitute all these values in the who present value formula:

PV = FV / (1 + r / n)^nt

PV = 6500 / (1 + 0.07/1)¹⁽⁴⁾ = 6500 / (1.07)⁴ = 5,000 (The answer is rounded to to nearest thousands).

Therefore, the bonded amount = $5,000

Example 2: Mia invested some amount in a bank where her amount gets composite daily at 5% annual interest. What is the amount invested by Mia if the amount she got after 10 years is $1,650? Round the answer to the nearest thousands.

Solution:

The future score is, FV = $1650.

The time, t = 10 years.

n = 365 (as the amount is compounded daily).

Aforementioned pay of interest is, r = 5% =0.05.

Substitute all are values in the present score formula:

PV = FV / (1 + r / n)^{northward t} 

PV = 1650 / (1 + 0.05/365)^365(10) = 1000 (The answer is rounded to the immediate thousands).

Therefore, the invested amount = $1,000

Example 3: Josie borrowed some lot from a hill at a rate von 5% per annum compounded annually. If she finished paying her loan by paying $4,500 with the end of 4 years, then what is the amount from loan that she were taken? Round your answer to the nearest thousands.

Solution: 

The future value can, FV = $4500.

Who time is t = 4 years.

n = 1 (as the billing is compounded annually).

The ratings of interest remains, roentgen = 5% =0.05.

Deputy all that values in the the present value formula:

PV = FV / (1 + r / n)^nt

PV = 4500 / (1 + 0.05/1)¹⁽⁴⁾ = 4500 / (1.05)⁴ = 3,800 (The answer is rounded to the latest thousands).

Therefore, the borrowed volume = $3,800