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1Fix the driver behind crashes, sound loss and screen glitches2Repair Windows errors before they cause bigger problems3Scan for outdated or missing drivers - takes under a minutePV, FV, and PMT solve different unknowns in the same time-value-of-money calculation: PV finds what future cash flows are worth now, FV projects a balance forward, and PMT finds a regular payment or deposit. In Excel and Google Sheets, the result is useful when payments are level, the rate is constant, and the timing is regular; matching the rate and number of periods is essential.
Choose the formula for the unknown
| Function | Solves for | Loan use | Savings use |
|---|---|---|---|
| PV | Value today | Estimate the principal supported by a regular payment | Find a starting balance for a future target |
| FV | Value at the end | Estimate a remaining or balloon balance | Project the value of a balance and regular deposits |
| PMT | Regular payment | Calculate a scheduled payment | Calculate the deposit needed for a target |
These functions are alternative ways to solve a cash-flow relationship, not unrelated formulas. If the unknown is the time required, use NPER; if it is the periodic rate, use RATE.
Understand the inputs and match their time units
- rate: interest rate per payment period.
- nper: total number of payment periods.
- pv: present value, or amount at the start.
- fv: future value, or amount remaining or targeted at the end.
- pmt: equal payment or deposit each period.
- type: timing; 0 or omitted means each period ends, and 1 means each period begins.
The rate and number of periods must use the same unit. For a nominal annual rate compounded monthly and monthly payments, use annual rate divided by 12 and years multiplied by 12. For quarterly payments, use annual rate divided by 4 and years multiplied by 4. Microsoft illustrates the monthly conversion with a four-year loan as annual rate divided by 12 and 48 periods: Microsoft’s PV function guidance.
Do not automatically divide an effective annual yield such as APY by 12. If the input is an effective annual rate and there are m compounding periods per year, the equivalent periodic rate is (1 + effective_annual_rate)^(1/m) - 1. Use the lender or account’s stated compounding convention where available; APR, nominal rate, and APY are not interchangeable.
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How the formulas relate
A single lump sum
For one amount growing or being discounted, FV = PV × (1 + r)^n and PV = FV / (1 + r)^n, where r is the periodic rate and n is the number of periods.
Equal recurring payments
For end-of-period payments (an ordinary annuity), the combined relationship is:
FV = PV(1 + r)^n + PMT × [((1 + r)^n − 1) / r]
For beginning-of-period payments (an annuity due), multiply the payment-stream contribution by (1 + r). Equivalently, the ordinary-annuity PV or FV for the payment stream is multiplied by (1 + r). Each payment has one extra period to accrue interest.
A compact master equation that includes timing is FV = PV(1 + r)^n + PMT × (1 + r × type) × [((1 + r)^n − 1) / r]. Spreadsheet functions solve this relationship for the requested value. At a zero rate, avoid the division by r in a hand-built formula: FV = PV + PMT × n, and PMT = −(PV + FV) / n.
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Spreadsheet syntax and cash-flow signs
Excel and Google Sheets use these core forms:
=PV(rate, nper, pmt, [fv], [type])=FV(rate, nper, pmt, [pv], [type])=PMT(rate, nper, pv, [fv], [type])
Square brackets indicate optional arguments, not characters to type. Omitted future value is treated as zero in the usual loan or investment calculation; omitted type means end-of-period cash flows. Google Sheets documents equivalent PMT syntax at Google Sheets PMT. Microsoft explains the function arguments and sign convention for PMT, PV, and FV.
Financial functions use cash-flow signs: money paid out is negative and money received is positive. In a borrower-perspective loan calculation, entering principal as positive makes the scheduled payment negative. In a savings-goal calculation, entering the target as a negative future cash flow can make the required deposit positive. Reversing all signs consistently gives the same magnitude. A negative result is therefore not automatically an error.
Calculate a loan payment with PMT
For a fully amortizing loan with monthly payments, no balloon balance, and a nominal annual rate compounded monthly:
=PMT(annual_rate/12, years*12, loan_amount)
For a $300,000 loan at 6.5% over 30 years, enter:
=PMT(6.5%/12, 30*12, 300000)
The result is approximately −$1,896.20 per month; the negative sign represents the borrower’s outflow. Use =ABS(PMT(6.5%/12, 30*12, 300000)) if a display-only positive amount is more convenient. This models principal and interest under the stated assumptions, not a complete housing bill: property taxes, insurance, lender fees, reserves, and other charges are not automatically included. Microsoft describes PMT as a payment calculation based on constant payments and a constant rate: PMT function documentation.
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If the loan is expected to have a balance left after the last scheduled payment, enter that ending balance as fv. For example, use =PMT(rate, nper, pv, -balloon_amount) when the principal is entered as a positive borrower-side inflow and the balloon is a borrower-side outflow. Check signs consistently against the cash-flow perspective.
Calculate a savings deposit with PMT
To find equal monthly deposits needed to reach a target from a zero starting balance, use:
=PMT(rate, nper, 0, -target)
For an $8,500 goal over three years at a nominal 1.5% annual rate with monthly periods, enter =PMT(1.5%/12, 3*12, 0, -8500). The required deposit is about $230.99 per month with end-of-month deposits. Microsoft gives this equivalent example in its guide to calculating payments and savings.
If there is already a balance, put it in pv with a sign opposite the target. For example, a saver’s existing balance can be entered as a negative cash outflow and the target as positive, or vice versa; maintain a consistent perspective so the returned PMT represents the deposit direction you expect.
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Project savings with FV
To project an ending balance from regular deposits and a starting balance, use:
=FV(rate, nper, -deposit, -starting_balance)
For $200 deposited at each month-end for 10 years at a nominal 5% annual rate compounded monthly, with no initial balance:
=FV(5%/12, 10*12, -200, 0)
The modeled result is approximately $31,056.46. Deposits total $24,000; the difference is interest under the assumed rate, timing, and compounding. To project only a lump sum, use =FV(rate, nper, 0, -starting_balance). FV is a scenario calculation, not a guarantee: rates can change, and withdrawals, taxes, or fees can change the outcome. See Microsoft’s FV function documentation.
Use PV to find a loan amount or starting balance
Loan principal supported by a payment
To estimate the present value of a fixed repayment stream, use =PV(rate, nper, -payment, 0, 0). For example, =PV(7%/12, 60, -500, 0, 0) estimates the principal supported by $500 monthly payments for 60 months at the modeled periodic rate. It is not a lender approval amount and excludes any costs not represented in the cash flows.
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Starting balance needed for a savings target
To find the current balance that, together with regular deposits, reaches a target, use =PV(rate, nper, -deposit, target, 0), adjusting signs to match the cash-flow perspective. Microsoft describes PV for both loan and investment calculations in its PV function reference.
Choose the right payment timing
Use type = 0 for payments at the end of each period and type = 1 for payments at the beginning. Thus =PMT(rate, nper, pv, fv, 0) and =PMT(rate, nper, pv, fv, 1) describe different schedules. Beginning-of-period deposits—such as some rent, lease, or savings arrangements—earn one additional period of interest per deposit compared with otherwise identical end-of-period deposits. Select timing from the actual schedule rather than choosing whichever result looks preferable.
Build an amortization schedule
PMT gives the level payment, but an amortization schedule shows how each payment is split. For a fixed-rate loan, each period can be calculated from the prior ending balance:
- Interest: beginning balance × periodic rate
- Principal: payment − interest
- Ending balance: beginning balance − principal
In a sheet, if the beginning balance is in B2, periodic rate in C1, and the positive payment amount in D1, use =B2*$C$1 for interest, =$D$1-E2 for principal (if E2 holds interest), and =B2-F2 for ending balance (if F2 holds principal). Carry each ending balance to the next row as the next beginning balance. Ensure the payment sign and balance convention are consistent.
=IPMT(rate, period, nper, pv, [fv], [type]) isolates a period’s interest, while =PPMT(rate, period, nper, pv, [fv], [type]) isolates principal. Google documents PPMT in Sheets. CUMIPMT and CUMPRINC can calculate cumulative interest and principal over a specified range of periods where supported by the spreadsheet application.
Common errors and checks
- Annual rate used with monthly periods: for a monthly 30-year calculation,
=PMT(6.5%, 360, 300000)mismatches units. With a nominal rate compounded monthly, use=PMT(6.5%/12, 30*12, 300000). - Years entered as nper: a 30-year monthly loan has 360 periods, not 30.
- Wrong sign on target or payment: reverse the cash-flow signs consistently; use ABS only to format a known outflow as a positive display.
- Zero rate in a hand formula: use the separate zero-rate relationship rather than dividing by zero.
- Premature rounding: keep the periodic rate, payment, and balance calculations unrounded internally; round for display or where the actual payment schedule explicitly rounds to cents.
- Unmodeled costs or contract details: daily accrual, day-count rules such as actual/365, payment timing, fees, prepayments, skipped or late payments, variable rates, and per-payment rounding can make an estimate differ from a lender’s payoff. The CFPB’s repayment examples use payment schedules and present-value annuity factors, illustrating why disclosures may require more than a single PMT calculation: Regulation Z Appendix M2.
Use these checks before relying on a result:
- At zero interest, a loan with no balloon should have payment equal to principal divided by number of periods.
- With no balloon, the scheduled principal paid over the full term should approximately equal the original principal, subject to rounding.
- With the same rate and deposits, beginning-of-period savings deposits should produce a higher FV than end-of-period deposits.
- At the same rate, a longer loan term generally lowers the scheduled payment but increases total interest.
When PV, FV, and PMT are not enough
These functions assume equal periodic cash flows and a constant rate. For changing deposits, missed payments, irregular dates, or variable rates, build a dated cash-flow schedule instead of treating PMT or FV as an exact forecast. NPV and IRR address periodic cash-flow series; XNPV and XIRR handle dated cash flows. RATE estimates the periodic rate implied by payment, term, present value, and ending value; NPER estimates the number of periods required. Consumer loan comparisons should also use the lender’s disclosed APR and total cost rather than relying on a basic PMT estimate alone.
Quick Recap
Quick reference
- Find a payment:
=PMT(rate_per_period, total_periods, pv, [fv], [type]) - Find a savings target deposit:
=PMT(rate_per_period, total_periods, 0, -target, [type]) - Project a balance:
=FV(rate_per_period, total_periods, -deposit, -starting_balance, [type]) - Find a supported principal:
=PV(rate_per_period, total_periods, -payment, [fv], [type]) - Find the time:
=NPER(rate, pmt, pv, [fv], [type]) - Find the implied rate:
=RATE(nper, pmt, pv, [fv], [type], [guess])
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