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

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.

### Answer: The expression is used to calculate the present value of an amount of money is PV = FV / (1 + r / n)^{n t}.

Let's look into the solution below.

**Explanation:**

Present value (PV) finds application 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)^{n t}

Dividing both sides by (1 + r / n)^{n t},

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 half-yearly.
- n = 4, if the amount is compounded quart-yearly.
- 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.