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Present value

How to compare money paid at different times.

FinanceMankiw ch. 14About 5 min: 2 reading, 3 practiceUpdated 27 October 2026

General education, not financial advice.

After this lesson you can

Work out a present value by dividing by (1 + r)ᴺ
Compare money paid at different times
Explain why higher rates lower present values

Money over time: lesson 2 of 5

Mankiw ch. 14
Compound interest 5 min
Present value 5 min
Mankiw ch. 11
Measuring inflation with a price index 4 min
Real and nominal interest rates 3 min
Bogle ch. 4
Costs and the market return 3 min

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Pairs with Mankiw, Principles of Macroeconomics (6th ed.), chapter 14, "The Basic Tools of Finance": present value

What it is

Money you have today can earn interest, so it is worth more than the same amount later. Present value turns a future amount into what it is worth today: the sum you would need to put away now, at today's interest rate, to end up with that future amount.

It is compound interest run backwards. Instead of multiplying by (1 + r)ᴺ, you divide:

present value = future amount ÷ (1 + r)ᴺ

Working out a present value is called discounting.

Quick check

Tap an answer to check it.

To turn a future amount into today's value, you…
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divide by (1 + r)ᴺ. Present value is compounding run backwards.

Why it matters

Present value lets you compare offers paid at different times, like a prize now or a bigger prize later, or a cost today against income in ten years. Businesses use the same idea to decide whether a project is worth paying for.

Worked example

Would you rather have 1,000 today or 1,500 in 8 years?

At 4% a year: 1,500 ÷ 1.04⁸ ≈ 1,096. The 1,500 is worth about 1,096 today, which is more than 1,000, so waiting wins.
At 7% a year: 1,500 ÷ 1.07⁸ ≈ 873. Now the 1,500 is worth less than 1,000 today, so taking the money now wins.

The same two offers give different answers, because the interest rate changes what waiting costs you.

Common mistake

Adding up future payments as if they were all paid today. A prize of 10,000 a year for 30 years is "300,000" on paper, but each later payment is worth less today, so its present value is well below 300,000.

Key terms

present value: what a future amount is worth today
discounting: working out a present value
interest rate: the price of waiting; higher rates shrink present values

Practise the key terms

Tap a card to turn it over. 3 cards.

Front	Back
present value	what a future amount is worth today
discounting	working out a present value
interest rate	the price of waiting; higher rates shrink present values

Practice

Quick quiz

Tap an answer to check it.

When interest rates rise, what happens to the present value of a fixed future payment?
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It falls. You divide by a bigger (1 + r)ᴺ, so today's equivalent is smaller.
What is the present value of 110 paid in one year, at 10% interest?
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100. 110 ÷ 1.10 = 100.

Work it through

You will be paid 2,420 in 2 years. Interest rates are 10% a year. What is it worth today?

(1.10)²
Present value

Practice problems

Basic

What is the present value of 1,050 paid in one year, at 5% interest?
Answer and full solution
Answer: 1,000
1. Divide by (1 + r) once: 1,050 ÷ 1.05 = 1,000.

Intermediate

What is the present value of 5,000 paid in 3 years, at 6% a year?
Answer and full solution
Answer: About 4,198.10
1. (1.06)³ = 1.06 × 1.06 × 1.06 ≈ 1.191016.
2. 5,000 ÷ 1.191016 ≈ 4,198.10.

Challenge

Offer A pays 900 today. Offer B pays 1,000 in 2 years. Interest rates are 6% a year. Which is worth more today, and by how much?
Answer and full solution
Answer: A, by about 10
1. Present value of B: 1,000 ÷ 1.06² = 1,000 ÷ 1.1236 ≈ 890.00.
2. A is 900 today, which is about 10 more than B's 890.
3. At a lower interest rate, B could win: try it in the calculator.

In short

Money today is worth more than the same money later.
Present value = future amount ÷ (1 + r)ᴺ.
Higher interest rates mean lower present values.
Compare offers paid at different times by their present values.

Mastery check

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Check yourself

Answer in your head first, then open the answer. Nothing is saved.

Why is 100 today worth more than 100 in five years?
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Money today can be saved and earn interest, so it grows into more than 100 by then.
What is the present value of 121 paid in two years, at 10% a year?
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100, because 121 ÷ 1.1² = 121 ÷ 1.21 = 100.
What is the name for working out a present value?
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Discounting.