APR Desk · Discounting

Present value calculator

What a future amount is worth today

A dollar later is worth less than a dollar now if you can earn a return in between. Present value is that idea as arithmetic. This page discounts either one future lump sum at an annual rate, or a string of equal end-of-month payments at a monthly rate.

Inputs

Result

Fill in the fields and press Calculate.

Disclaimer: A discounting sketch. It is not an appraisal of an investment.

How to use

  1. Choose a lump sum or a monthly payment. The unused dollar box is ignored.
  2. Enter the annual rate and the number of years.
  3. For a lump sum, fill the future amount. For payments, fill the monthly payment.
  4. Press Calculate. The hero is the value today.

How it's calculated

Lump sum: present value = future amount ÷ (1 + annual rate)^years. The rate compounds once a year in this mode.

Annuity: the monthly rate is the annual rate divided by 12, and the count of payments is years times 12, rounded. Present value = payment × (1 − (1+r)^−n) ÷ r. Payments are treated as arriving at the end of each month. A zero rate uses payment × n.

Worked example

Ten thousand dollars due in 10 years at 5 percent a year is worth about $6,139.13 today, because 10,000 ÷ (1.05)^10 is that figure. Five hundred dollars at the end of each month for 10 years at 5 percent is worth about $47,140.68 today.

Assumptions

A constant rate. The lump sum compounds yearly. The annuity compounds monthly and pays at month-end. No fees and no missed payments.

FAQ

Which box do I fill?

Fill the future amount for a lump sum, or the monthly payment for an annuity. Leave the other at blank or zero.

Why is today's value lower than the future amount?

The rate you typed is treated as money you could earn while you wait. A higher rate makes the same future dollar worth less today.

Is this the loan amount I can borrow?

A loan that supports a payment is the affordability calculator. This page discounts a future amount or a payment stream. The formulas rhyme and the questions differ.

What if payments arrive at the start of the month?

This annuity is end-of-month. A start-of-month annuity is worth one extra period of interest, and this form does not add that.

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