Which expression is used to calculate the present value of an amount of money?

Solution:

The term “present value” refers to the application of the time value of money that discounts the future cash flow to arrive at its present-day value. 

Present value (PV) finds application in finance to calculate the present-day value of an amount that is received at a future date. The present value expression is derived from the compound interest formula. The compound interest formula is,

FV = PV (1 + r / n)^nt 

Dividing both sides by (1 + r / n)^nt, we get,

PV = FV / (1 + r / n)^nt 

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 half-yearly.
• n = 4, if the amount is compounded quarterly.
• 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's take an example to understand this.

Example: Future value = $1650, t = 10 years, Annual interest rate = 5% where the amount is compounded daily. Calculate the present value.

Solution:

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).

Thus, the invested amount or present value = $1,000.

Hence, the expression used to calculate the present value is PV = FV / (1 + r / n)^{n t} .

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Which expression is used to calculate the present value of an amount of money?

Summary:

The expression which is used to calculate the present value of an amount of money is PV = FV / (1 + r / n)^nt.