What is the time value of money (TVM)?
TVM is the financial principle that a dollar today is worth more than a dollar in the future because today's dollar can be invested to earn a return. Every TVM problem links five variables — present value (PV), future value (FV), interest rate per period (r or i), number of periods (n), and periodic payment (PMT) — through the compound-interest equation. Given any four, you can solve for the fifth. This calculator handles the standard lump-sum and annuity cases.
What does each TVM variable mean?
PV is the amount you have or owe today. FV is the amount the account will be worth at the end of the term. r (or i) is the interest rate per compounding period, expressed as a decimal — divide an annual rate by the number of periods per year. n is the total number of compounding periods, which is years times periods per year. PMT is the recurring cash flow each period; set it to zero for single-sum problems.
What is the sign convention used in Excel and HP financial calculators?
Cash inflows are positive and outflows are negative, from your perspective. If you deposit $10,000 today, enter PV as -10,000 in Excel's FV(rate, nper, pmt, pv) function, and the returned FV will be positive — money that comes back to you. Mixing signs incorrectly is the most common reason Excel returns #NUM! or the wrong-sign answer. This widget hides the convention internally but the math underneath follows the same rules.
Why do financial functions matter outside of finance class?
Almost every recurring money decision is a TVM problem: mortgages, car loans, student loans, retirement contributions, lease-vs-buy comparisons, bond pricing, and even insurance payouts. Once you can move a cash flow forward or backward in time using PV and FV, you can compare offers on an apples-to-apples basis — for example, a $10,000 lump sum today versus $1,200/year for 10 years. TVM is the foundation of NPV, IRR, and most corporate finance analysis.
What is the difference between simple and compound interest in TVM?
Simple interest uses I = P × r × t, so interest is earned only on the original principal. Compound interest uses FV = PV × (1 + r)^n, so each period's interest is added to the balance and itself earns interest next period. Most real-world products — savings accounts, mortgages, bonds, retirement accounts — use compounding. The gap widens dramatically with time: $10,000 at 5% for 30 years grows to $25,000 with simple interest but $43,219 with annual compounding.
How do I convert an annual rate to a periodic rate?
Divide the nominal annual rate by the number of compounding periods per year and multiply n correspondingly. A 6% APR compounded monthly becomes r = 0.06/12 = 0.005 per month, with n = years × 12. For more precise effective-rate work, use EAR = (1 + APR/m)^m − 1, which gives the true yearly yield. Banks must disclose APY (a synonym for EAR) under the US Truth in Savings Act so consumers can compare accounts.
Can this calculator solve for the interest rate or number of periods?
The current widget solves for FV and PV given the other inputs. To solve for r or n, you typically need an iterative method because the TVM equation is non-linear in those variables — that's why Excel uses RATE() and NPER() as separate functions. As a workaround, enter trial values for r or n and adjust until the FV matches your target, or use Excel/Google Sheets RATE(nper, pmt, pv, fv) and NPER(rate, pmt, pv, fv) directly.
