Finance Calculator

Almost every money question with a time element, such as a loan, a savings plan, a pension or a lease, can be reduced to the same five quantities. Fill in the four you know, choose the one you want, and the calculator does the algebra. Signs matter: treat money that leaves your pocket as negative and money that comes back to you as positive, just as a financial calculator does.

With the default inputs, $20,000 is deposited at 6% a year and $2,000 is withdrawn at the end of each year for 10 years. The schedule shows the balance shrinking each period as the withdrawals outpace the interest, leaving about $9,455.36 at the end. The negative FV means that remaining amount would flow back to you.

The Time Value of Money (TVM)

A dollar today is worth more than a dollar promised later. Money in hand can be saved or invested and start earning a return immediately, while a future payment carries the risk that it arrives late, arrives smaller than promised or does not arrive at all. Inflation adds a third reason: prices tend to rise, so the same dollar buys less as time passes. This idea, called the time value of money, is the foundation of nearly every pricing decision in finance, from how a bank sets a mortgage payment to how an investor values a company's future cash flows.

To compare amounts that occur at different times, finance moves them to a common date. Moving money forward in time is compounding: $1,000 invested at 6% grows to $1,060 after one year and about $1,790.85 after ten. Moving money backward is discounting: $1,790.85 due in ten years is worth $1,000 today at a 6% discount rate. The discount rate you choose reflects what you could earn elsewhere with similar risk, which is why a riskier promise is worth less today than a safe one of the same size.

Five variables describe a standard TVM problem. N is the number of compounding or payment periods. I/Y is the nominal interest rate per year. PV, the present value, is the amount at the start. PMT is a level payment made every period, such as a loan installment or a regular deposit. FV, the future value, is the amount left at the end. Two settings complete the picture: P/Y, the number of payments per year, and C/Y, the number of times interest compounds per year. When P/Y and C/Y differ, the rate per payment period is found by converting the yearly rate to its compounding period and then to the payment period.

Solving for FV answers questions like how much a savings plan will be worth at retirement. Solving for PV tells you what a future stream of payments is worth today, which is how bonds and annuities are priced. PMT gives the installment on a loan or the deposit needed to reach a goal. I/Y reveals the actual return or borrowing cost buried in a deal, and N tells you how long a goal or a repayment will take. FV, PV, PMT and N can be found with algebra; I/Y has no closed-form solution once payments are involved, so calculators find it by trial and refinement, as this one does.

PV(1 + i)ᴺ + PMT(1 + i·k)[(1 + i)ᴺ − 1] ÷ i + FV = 0

PV

present value (money in is positive, money out negative)

PMT

payment each period

FV

future value

N

number of periods

i

rate per payment period, (1 + I/Y ÷ C/Y)^(C/Y ÷ P/Y) − 1

k

1 if payments are made at the beginning of each period, 0 if at the end

The equation balances every cash flow in and out. The calculator solves it directly for FV, PV, PMT and N, and numerically for I/Y.

PMT

PMT is the fixed amount paid or received every period. Loans, leases, annuities and systematic savings plans all have one. On a mortgage, PMT is the monthly principal-and-interest installment; on a retirement plan, it is the regular contribution or withdrawal. A PMT of zero turns the problem into a simple lump-sum compounding question.

Timing changes the answer. Payments at the end of each period, called an ordinary annuity, are the norm for loans. Payments at the beginning, called an annuity due, are common for rent, leases and many savings plans, and because each payment has one extra period to earn interest, an annuity due is always worth more than an ordinary annuity with the same payment. Use the beginning and end toggle to switch between the two.

Finance Class

Introductory finance and accounting courses spend weeks on TVM problems, and exams such as the CFA, CFP and actuarial tests assume students can solve them quickly. Students usually learn on a dedicated device such as a Texas Instruments BA II Plus or an HP 12C, which use the same five-key layout and sign convention as this calculator. Working a few problems here and checking them on paper with the formula is a good way to build intuition before an exam.

The Importance of the Finance Calculator

TVM math appears in more everyday decisions than most people notice. Comparing a car loan with a cash rebate, deciding whether to pay points on a mortgage, working out how much to save each month for a child's education, or checking whether a pension's lump sum is a fair trade for its monthly payments are all TVM problems. Spreadsheets have equivalent functions (FV, PV, PMT, RATE and NPER), but a purpose-built calculator keeps the inputs visible and the signs consistent.

The results are only as good as the assumptions. Real interest rates change, payments are skipped or increased, and fees and taxes nibble at returns. Treat the answer as a baseline and test a few different rates and periods to see how sensitive your plan is.

Frequently asked questions

Sources

• Investor.gov – Financial Tools and Calculators
• Consumer Financial Protection Bureau