TVM calculator: solve any time value of money problem
Enter four of the five time value of money values, the number of periods, the interest rate, the present value, the payment and the future value, and the calculator solves the fifth, with an amortization schedule when there is a payment. A $500,000 loan at 4.5% over 300 monthly payments costs $2,779.16 a month, and $10,000 invested with $500 a month at 6% grows to $264,122.49 in 20 years.
Time value of money
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How to use the TVM calculator
Choose what to solve for, fill in the other four values and press Calculate. Your inputs are kept in the page address, so a shared link opens with the answer already worked out.
The value you want. Its field is greyed out while the calculator solves it. The starting value is FV.
The total number of payment periods, not years: 360 monthly periods is 30 years. The label changes with the payment frequency.
The annual interest rate as a percentage, for example 5 for 5%.
The amount today, the payment each period and the amount at the end. Money you pay out is negative and money you receive is positive: invest $300,000 today and PV is −300,000.
Monthly, quarterly, semi-annual or annual. Interest compounds once per payment period.
End of period for most loans, or beginning of period when each payment is made up front.
How to read your result
The answer appears at the top, followed by every value in the calculation and, when there is a payment, the schedule of how each payment splits between interest and principal.
The answer
The solved value, in the same sign convention you entered. A payment shown as negative is money you pay out. The rate is shown to four decimals and periods to two, so 262.04 months means 262 full payments and a smaller final one.
All values
The full set of five, with the solved one highlighted. Check the signs here first if a result looks wrong: a PV and an FV with the same sign usually mean one was entered the wrong way round.
Amortization schedule
Each period's payment, the interest in it, the principal it repays and the balance left. Long schedules show the first 6 and last 3 periods, enough to see how early payments are mostly interest and later ones mostly principal.
Errors
If the calculator reports that no solution exists, the values cannot all be true at once, usually because of a sign. Solving for a rate works by repeated estimates; if no rate fits the values you entered, the calculator says so.
Five questions, one calculator
Each row is a real calculation in the tool, with monthly payments at the end of each period.
Before tax and inflation. The lump-sum row assumes a steady 5% return and spends the capital to zero.
Time value of money in a retirement plan
The question everyone asks is how much you need saved to produce it. The honest answer is that the question is missing a variable.
Kaetyn St. Hilaire, CFA, in What it actually takes to retire on $8,500 a month in Canada
Most retirement questions are time value of money questions underneath: how much capital an income needs, what a savings rate grows to, how long a portfolio lasts at a given withdrawal. The calculator gives the clean answer with a steady return and no tax.
The real answer adds tax, the order of returns, CPP and OAS, and which accounts the money comes from. What it actually takes to retire on $8,500 a month shows how much those change the capital needed, and the CPP calculator handles the government pension.
Turning the clean answer into a plan you can follow is the work of financial planning in Calgary with Kaetyn.
Kaetyn on YouTube: What It Actually Takes to Retire on $8,500 a Month in Canada
TVM calculator questions
Answers drawn from the calculator's own rules and assumptions.
A time value of money calculator relates five values: the number of periods (N), the annual interest rate (I/Y), the present value (PV), the payment each period (PMT) and the future value (FV). Enter any four and it solves the fifth, so the same tool works out a loan payment, a savings goal, the lump sum an income needs or how long a debt takes to repay.
The calculator follows the cash. Money you pay out, such as a deposit, an investment or a loan payment, is negative. Money you receive, such as loan proceeds or a withdrawal, is positive. If every value has the same sign there is no solution, which is the most common reason for an error.
Yes. Set PMT to 0 to grow a single deposit, or enter a regular deposit as a negative PMT, then solve for FV. $10,000 today plus $500 a month at 6% for 20 years, compounded monthly, grows to $264,122.49.
This calculator compounds once per payment period, so a monthly payment compounds monthly. Canadian fixed-rate mortgages are calculated with semi-annual compounding, which gives a slightly lower payment: $2,767.36 a month instead of $2,779.16 on $500,000 at 4.5% over 25 years. The mortgage affordability calculator uses semi-annual compounding.
End of period is an ordinary annuity: payments arrive at the end of each period, as with most loans. Beginning of period is an annuity due: payments arrive at the start, as with rent or a deposit made on the first of the month. Payments at the start earn one more period of interest.
Related articles
- What it actually takes to retire on $8,500 a month in Canada Capital needed for an income
- How much do you actually need to retire in Canada? Spending once the mortgage is paid
- How much you need to never run out of money in retirement Withdrawals that last
- What does it look like to retire in Canada with $1.5 million? What a portfolio supports
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