Present value and the time value of money

What you will learn

Put both choices on the same date before comparing them. If money can earn interest, ₹1,000 now can become more than ₹1,000 a year from now. The amount you would need to set aside now for a future payment is its present value.

Read the full lesson guide

Present value = future amount ÷ (1 + rate)ⁿ

Money available today can earn a return before a future payment arrives. To compare two choices, move both to the same date. Multiplying by the growth factor moves cash forward. Dividing moves it backward. Match the rate to the length of each period. If you can earn 10% in a year, ₹1,000 today grows to ₹1,100. Those amounts are equivalent under that assumption.

If you can earn 10% in a year, ₹1,000 today grows to ₹1,100. Those amounts are equivalent under that assumption.

Which is worth more today at a positive rate, ₹1,000 today or ₹1,000 next year?

Full lesson guide

How the idea works

Present value: What a future payment is worth today under your assumptions.
Discount rate: The rate you use to bring future money back to today.

Apply it to a decision

Fictional example · Compare two payments for an equipment sale

A customer offers ₹95,000 today or ₹110,000 in two years. Use an 8% annual rate and assume both payments are equally certain.

Which offer is worth more today?

Set up the problem. Discount the payment due in two years over two periods.
Work it out. Present value = ₹110,000 ÷ 1.08² ≈ ₹94,307.
Read the result. Take ₹95,000 today on these assumptions. It is worth about ₹693 more than the delayed offer.

Before you use it

Move every payment to the same date. Match the rate and period count.

Common mistake. Comparing future and current rupees directly gives the wrong result.

Read or watch next

MIT OpenCourseWare video · Present value
Start with Part I. Notice how the lecturer places each payment on a date.

Topic cheat sheet

Core idea: Compare money paid or received on different dates.
Formula or rule: Present value = future amount ÷ (1 + rate)ⁿ
Money available today can earn a return before a future payment arrives. To compare two choices, move both to the same date. Multiplying by the growth factor moves cash forward. Dividing moves it backward. Match the rate to the length of each period. If you can earn 10% in a year, ₹1,000 today grows to ₹1,100. Those amounts are equivalent under that assumption.
How to approach it: Move every payment to the same date. Match the rate and period count.
Common mistake: Comparing future and current rupees directly gives the wrong result.

Interview recall prompt

Why does a higher discount rate reduce present value?

OpenStax · Principles of Finance

Try the worked case