How do you calculate present value and future value in finance?

Present Value and Future Value in Finance

Present Value (PV) and Future Value (FV) are fundamental concepts in finance used to compare the value of money at different points in time, accounting for interest rates.

• Future Value (FV): The amount an investment will grow to after earning interest over a period.
• Present Value (PV): The current worth of a future sum of money, discounted by an interest rate.

Key Formulas

• Future Value:

$$ FV = PV \times (1 + r)^n $$

• Present Value:

$$ PV = \frac{FV}{(1 + r)^n} $$

Where:

• $PV$ = Present Value
• $FV$ = Future Value
• $r$ = interest rate per period (as a decimal)
• $n$ = number of periods

---

Worked Example

Question:
Suppose you want to know how much you need to invest today (PV) to have $2,000 in 5 years, if the annual interest rate is 6%.

Step 1: Identify variables

• $FV = 2000$
• $r = 0.06$
• $n = 5$

Step 2: Apply the PV formula
$$ PV = \frac{2000}{(1 + 0.06)^5} $$

Step 3: Calculate denominator
$$ (1 + 0.06)^5 = 1.3382255776 $$

Step 4: Compute PV
$$ PV = \frac{2000}{1.3382255776} \approx 1,494.57 $$

Interpretation:
You need to invest approximately $1,494.57 today at 6% annual interest to have $2,000 in 5 years.

---

Takeaways

• Present Value discounts future cash flows to today using the interest rate.
• Future Value projects today's money into the future by compounding.
• These calculations help compare monetary values across different times.