Present and Future Value With PV and FV

A dollar today is worth more than a dollar next year, because today's dollar can earn interest. This idea is called the time value of money.

Two functions capture it. PV (present value) tells you what a future stream of money is worth right now. FV (future value) tells you what money today will grow into later.

They are mirror images of each other.

Future value uses =FV(rate, nper, pmt, [pv], [type]).

• rate — interest rate per period.
• nper — number of periods.
• pmt — the payment made each period (0 if none).
• pv — optional starting lump sum.
• type — optional, 0 for end, 1 for start of period.

You must include pmt even when it is zero, because pv comes after it.

Suppose you invest 1,000 today at 5% annually for 10 years with no further contributions.

There is no recurring payment, so pmt is 0. The starting amount is your pv, entered as a negative because it leaves your pocket.

The formula returns about 1,628.89 — your savings after a decade of compounding.

Most savings plans add money every period. Put that contribution in the pmt argument.

If you deposit 200 at the end of each year for 10 years at 5%, with no starting balance, FV totals both your deposits and their compounded growth.

This returns roughly 2,515.58 — far more than the 2,000 you actually paid in.

You can model both at once: a starting balance and regular deposits. Fill in both pmt and pv.

Start with 1,000, add 200 every year, at 5% for 10 years. FV grows the lump sum and the deposits together.

Both inputs are negative because both are cash leaving you and going into the investment.

PV answers the reverse question: what is a future amount worth today? Its syntax is =PV(rate, nper, pmt, [fv], [type]).

Imagine you are promised 10,000 in 5 years. At a 5% discount rate, that promise is worth less today.

The formula below shows roughly -7,835.26 — the amount you would invest now to reach 10,000.

PV can also value a series of equal payments — an annuity. Put the recurring amount in the pmt slot.

What is it worth today to receive 1,000 per year for 10 years at 5%? PV discounts each future payment back and sums them.

The answer is about 7,721.73, less than the 10,000 of raw payments because future dollars are discounted.

Just like PMT, both PV and FV require the rate and nper to share a period.

For monthly compounding, divide the annual rate by 12 and multiply the years by 12.

Monthly savings of 100 at a 6% annual rate for 5 years uses rate 0.06/12 and 60 periods.

The cash-flow rule still holds. Outflows are negative, inflows are positive.

When you deposit money (FV) or invest today (PV), those amounts are negative. The result FV returns is positive because you eventually receive it.

If your numbers come out with an unexpected sign, check that you marked deposits as negative.

Because they are inverses, PV and FV undo each other. If you take an FV result and feed it back through PV with the same rate and nper, you return to the original amount.

Invest 1,000 today, grow it for 10 years at 5% with FV, then discount that result with PV — you land back near 1,000.

This makes them a handy way to sanity-check a financial model. Both behave identically in Excel and Google Sheets.

Because deposits are negative, FV results come out positive — that is usually what you want for a savings balance. But sometimes signs get confusing in a report.

You can always wrap the result in ABS to force a clean, positive figure regardless of input signs.

For example, the value of a 10-year savings plan can be shown as a tidy positive number for a dashboard cell.

Test your grasp of present versus future value.

You learned the two time-value functions.

• FV(rate, nper, pmt, pv) grows money forward in time.
• PV(rate, nper, pmt, fv) discounts future money back to today.
• Use pmt for recurring deposits, pv/fv for lump sums; include both for combined plans.
• Outflows are negative; match rate and nper to the same period.

They are mirror images and work the same in Excel and Google Sheets.