Time Value of Money Calculator

The Time Value of Money is an important financial concept to master to make better financial decisions. It considers that invested money grows and can generate cash flows in the future (for you or for your banker). The future value is calculated by a function that multiplies the cash invested by the expected rate of return and the length of time that will pass before accessing the money. Similarly, the present value of future cash flows can be calculated by dividing the cash flows by the amount of time and the expected interest rate.

The TIME MACHINE is very sophisticated software that can handle thousands of parameters at a time for calculations, but for simple TVM problems, you can use this calculator modelled on my TI BA II Plus Financial calculator (an actual physical calculator. Outdated I know, but these are still used for CFA, CFP, CPA and such financial exams). It solves TVM problems with equal and regular cash flows that are either all inflows or all outflows (for example annuities, loans, mortgages, leases, and savings). We also added support for growing annuities, where the payment grows regularly every period by a fixed percentage.

The potential inputs for a TVM calculations are the present value (PV), the regular payment if any (PMT) (and its growth rate if a growing annuity), the future value (FV), the nominal annual interest rate (I/Y) (and how often it is compounded), and finally, the total number of periods (N, which is the number of payments per year multiplied by the number of years if more than one year). You can solve for any one of these variables, given the other 4. You can also select whether payments are made at the beginning or at the end of each period.

The only trick to it is that you have to think in terms of cash flows to you. Enter money you give to the bank (to save or to pay off a loan) as a negative number, and any money you get from the bank (as a loan or withdrawal from savings) as a positive amount.

The interest, payment, and balance at the end of each period is shown in a table, like a mortgage amortization table, that details the money's growth and the cash flows.

ChatTVM

Although simple in concept, TVM problems take getting used to, to do them correctly in practice. To make it easier, you can now type in a word description of your TVM problem instead of using the form. We use the AI''s ability to understand language to get the necessary information from your query to feed to our calculator (as AI language models are terrible at math on their own). We then run our accurate TVM calculator for you given the inputs fed from the AI language model. Some examples of the types of queries you can ask:

  1. My mortgage is $300,000 at 5 percent interest per year with semi-annual compounding. If I make bi-weekly payments of $1000, when will the mortgage be paid off?
  2. If I invest $7000 per year in a TFSA growing at 6 percent a year, how much will it be worth in 10 years?
  3. I have a pension that pays me a $1000 a month until I die. If I die in 30 years, assuming the interest rate is 4 percent per year, what is the present value of the annuity?
  4. I have a million dollars in investments growing at 5 percent per year. How much can I spend per year and die leaving $200,000 in 35 years?
  5. My parents bought their home 20 years ago for $200,000. It is now worth $1,000,000. What has been their annual rate of return assuming annual compounding?

The beauty of this is that you can then see the appropriate entries put in the form for the calculator, including the solution for the missing value you're asking for. Can you identify which variable each example question is solving for? (1: N, 2: FV, 3: PV, 4:PMT, 5:I/Y). I think this will be very helpful to learn how to use a TVM calculator and master these kinds of problems.

This assumes the AI understood you well enough. You may have to refine your question or correct the entries. Sometimes the AI hallucinates the entries, particularly if the question is ambiguous or is missing information. You want be precise as possible in your question. In particular, specify the term for the interest rates (say percent per year or per month, for example) or it might make it up. Sometimes it has trouble confusing frequencies of events: the payment frequency, nominal quoted interest frequency, and the compounding of interest frequency. In the example #1 these are pretty clear (bi-weekly payments, quoted rate is annual, and compounding is semi-annual). It usually gets it right but not always (or not always the first time). Always double check the form output.

Don't ask too much of it. For now, It cannot do any intermediate calculations (like computing the number of years between two dates, or even any simple mathematical operations). Complex TVM problems may require breaking up into smaller TVM problems the calculator can handle. You may need to rephrase your question so that intermediate calculations are not required and break up the complex problems yourself. You can then use the ChatTVM multiple times to get to the correct final answer.

Solving even complex problems is possible with AI as we can instruct it by to write a program to solve the problem and run it. I found that although that approach can work well, it is very unreliable, even in fairly simple cases. For now on the MoneyReady App we are just getting the AI to run the program that I wrote that simply emulates the physical TI BA II Plus Financial calculator's TVM calculations.

However if you have a subscription to OpenAI's ChatGPT Plus, make sure their Code interpreter tool is active and you can ask it any TVM or other math problems. It's more interactive, and it will even show you the program it wrote to solve the problem. As mentioned its not entirely reliable yet, if you get an answer you have to double check-it carefully using a calculator or spreadsheet (or write your own program).

It's still early days, so I won't get rid of my TI BA II Plus just yet, but I have found the AI already quite impressive despite all the caveats mentioned. Have fun with it!