Future Value of $10,000 + $200/mo for 5 years at 12%
The exact future value for $10,000 + $200/mo for 5 years at 12%. Adjust any field below to solve for a different time-value-of-money variable or try your own numbers.
Solved For
Future Value (FV)
N
60
I/Y
12%
P/Y
12
PV
-$10,000.00
PMT
-$200.00
FV
$34,500.90
Result
With N = 60, I/Y = 12%, PV = ($10,000.00), PMT = ($200.00), and FV = $34,500.90, the Future Value (FV) above balances the time-value-of-money equation.
Account value over time
What is a Finance (TVM) Calculator?
The time value of money is the core idea behind all interest, loan, and investment math: a dollar today is worth more than a dollar in the future, because today's dollar can be invested and earn a return. Every loan payment, savings plan, and retirement projection reduces to the same five-variable equation linking Present Value (PV), Future Value (FV), the recurring Payment (PMT), the Number of periods (N), and the Interest rate per year (I/Y).
This calculator is a general-purpose TVM solver, the same tool built into financial calculators like the HP 12C or TI BA II Plus: enter any 4 of the 5 values and leave the one you want solved for blank. That flexibility means one tool answers very different questions — "what will my savings grow to?" (solve FV), "what payment do I need to hit a goal?" (solve PMT), "how long will it take?" (solve N), or "what return am I actually getting?" (solve I/Y).
How This Grows Over Time
A snapshot of the account balance at several points between now and 60 periods from now, for $10,000 + $200/mo for 5 years at 12%.
| Period | Balance |
|---|---|
| 0 | $10,000.00 |
| 1 | $10,300.00 |
| 2 | $10,603.00 |
| 3 | $10,909.03 |
| 4 | $11,218.12 |
| 5 | $11,530.30 |
| 6 | $11,845.60 |
| 7 | $12,164.06 |
| 8 | $12,485.70 |
| 9 | $12,810.56 |
| 10 | $13,138.66 |
| 11 | $13,470.05 |
| 12 | $13,804.75 |
| 13 | $14,142.80 |
| 14 | $14,484.23 |
| 15 | $14,829.07 |
| 16 | $15,177.36 |
| 17 | $15,529.13 |
| 18 | $15,884.42 |
| 19 | $16,243.27 |
| 20 | $16,605.70 |
| 21 | $16,971.76 |
| 22 | $17,341.48 |
| 23 | $17,714.89 |
| 24 | $18,092.04 |
| 25 | $18,472.96 |
| 26 | $18,857.69 |
| 27 | $19,246.27 |
| 28 | $19,638.73 |
| 29 | $20,035.12 |
| 30 | $20,435.47 |
| 31 | $20,839.82 |
| 32 | $21,248.22 |
| 33 | $21,660.70 |
| 34 | $22,077.31 |
| 35 | $22,498.08 |
| 36 | $22,923.06 |
| 37 | $23,352.29 |
| 38 | $23,785.82 |
| 39 | $24,223.68 |
| 40 | $24,665.91 |
| 41 | $25,112.57 |
| 42 | $25,563.70 |
| 43 | $26,019.33 |
| 44 | $26,479.53 |
| 45 | $26,944.32 |
| 46 | $27,413.77 |
| 47 | $27,887.90 |
| 48 | $28,366.78 |
| 49 | $28,850.45 |
| 50 | $29,338.95 |
| 51 | $29,832.34 |
| 52 | $30,330.67 |
| 53 | $30,833.97 |
| 54 | $31,342.31 |
| 55 | $31,855.74 |
| 56 | $32,374.29 |
| 57 | $32,898.04 |
| 58 | $33,427.02 |
| 59 | $33,961.29 |
| 60 | $34,500.90 |
The TVM Formula
Where i is the interest rate per period (I/Y ÷ 100 ÷ P/Y) and type is 0 for payments at the end of each period (the common case) or 1 for payments at the beginning (annuity due). Solving this single equation for whichever variable is missing covers every standard loan, savings, and annuity calculation.
Sign Convention: Why PV or PMT Is Negative
Financial calculators use a strict cash-flow sign convention: money that leaves your pocket is negative, money that comes back to you is positive. If you invest $10,000 today, PV is -10,000 because that cash is going out; the FV the calculator solves for comes back positive, because that's cash you'll eventually receive. For a loan, it flips — PV is positive (you receive the loan proceeds) and PMT is negative (you pay it back). Getting the signs backwards is the single most common mistake with TVM calculators, and it usually shows up as a wildly wrong-looking answer rather than an error message.
Solving for the Interest Rate or Number of Periods
Four of the five TVM variables — PV, FV, PMT, and N — can be isolated algebraically once the other four are known. The interest rate cannot: there's no way to rearrange the TVM equation to put I/Y by itself on one side, because it appears inside an exponent and inside a fraction at the same time. Solving for the rate (or, in some edge cases, for N) instead uses an iterative numerical search that narrows in on the answer step by step until the TVM equation balances to within a tiny tolerance — the same approach financial calculators have used internally for decades.
Ordinary Annuity vs. Annuity Due
Most loans and savings plans are ordinary annuities — the payment happens at the end of each period (you make March's loan payment at the end of March). An annuity due flips that timing so the payment happens at the start of the period instead — common for rent and insurance premiums, which are usually paid in advance. Because an annuity-due payment sits in the account for one extra period, it compounds slightly more, so the same numbers produce a marginally higher future value under the "payments at beginning" setting.
Example — Your Current Inputs
With N = 60, I/Y = 12%, PV = ($10,000.00), PMT = ($200.00), and FV = $34,500.90, the Future Value (FV) above balances the time-value-of-money equation.
Additional Example — A Car Loan
A $25,000 car loan (PV = 25,000, positive because it's cash received) is paid off over 5 years (N = 60 monthly periods) at 6% annual interest (I/Y = 6), with the loan fully repaid at the end (FV = 0). Solving for PMT gives a monthly payment of about $483.32 (shown as negative, since it's cash paid out each month) — exactly the number a dealership's loan calculator would quote.
About These Parameters
- N — Number of Periods
- The total number of compounding/payment periods over the life of the loan or investment — not years. At monthly compounding (P/Y = 12), 10 years is N = 120.
- I/Y — Annual Interest Rate
- The nominal annual interest rate as a percentage. This calculator divides it by P/Y to get the rate charged or earned per individual period.
- PV — Present Value
- The value of the cash flow today — a lump-sum investment (negative) or loan proceeds received (positive).
- PMT — Payment per Period
- The recurring cash flow each period — a contribution you add (negative) or a loan payment you receive (positive). Enter 0 if there's no recurring payment at all.
- FV — Future Value
- The value of the cash flow at the end of N periods — what an investment grows to, or what balance remains on a loan (0 for a fully amortizing loan).
- P/Y — Periods per Year
- How many compounding/payment periods happen each year — 12 for monthly (the most common case), 4 for quarterly, 1 for annually.
Frequently Asked Questions
Why did I get a "no valid solution" error?
This almost always means the cash-flow signs contradict each other — for example, PV, PMT, and FV all entered as positive numbers with no negative cash flow anywhere. A real financial scenario always has money flowing in one direction at some point and out at another; double-check that at least one of PV/PMT/FV is negative.
Can this calculator solve a simple loan payment or savings goal?
Yes — a loan payment is "solve for PMT" with PV positive and FV = 0; a savings goal is "solve for PMT" or "solve for FV" with PV negative (or 0) and PMT negative (money you contribute). The five-variable TVM equation underlies both.
Why is solving for the interest rate slower or less exact than the others?
The rate appears both inside an exponent and inside a fraction in the TVM equation, so there's no algebraic formula to isolate it directly. This calculator instead narrows in on the answer numerically until the equation balances to within a tiny tolerance — accurate for all practical purposes, but computed differently than the other four variables.
What's the difference between P/Y and N?
P/Y is how many periods happen in one year (12 for monthly); N is the total number of periods over the entire term. A 10-year monthly loan has P/Y = 12 and N = 120 — N is always P/Y multiplied by the number of years.