Chapter 4 Finance
4.6 TVM Solver Calculator
Learning Objective
By the end of this section, you will be able to:
- Solve annuities, payout annuities, and loans problems with the TVM Solver application
This section presents an alternate way to solve annuities, payout annuities, and loans problems using a Time Value Money Solver (TVM Solver) application. The examples and exercises in this section are the same examples and exercises from Sections 4.2 through 4.5. There are many applications that exist, but one free resource is the Geogebra TVM Solver. You can use the link to open a new webpage with the calculator, or use the one located in the Back Matter of this textbook.
TVM Solver
[latex]N[/latex] is the total number of payments that are made.
[latex]I\%[/latex] is the interest rate, written as a percentage.
[latex]PV[/latex] is the present value. [latex]PV=0[/latex] when you are trying to save money (for example, in savings annuities).
[latex]PMT[/latex] is the payment amount. PMT will always be a negative number when you are typing it into the TVM Solver.
[latex]FV[/latex] is the future value. [latex]FV=0[/latex] when you are paying something off (for example, in payout annuities and loans).
[latex]P/Y[/latex] is the number of payments per year.
[latex]C/Y[/latex] is the number of times the interest is compounded per year.
Note: [latex]P/Y[/latex] and [latex]C/Y[/latex] are always going to be the same number. Some problems may not specify the number of times the interest is compounded per year, and in that case, you will use the same number that you use for [latex]P/Y[/latex].
Finding Interest
In annuities problems, the goal is to save money, meaning [latex]PV[/latex] will be 0 because there is no money in the account when it opens, and [latex]FV[/latex] will always be a value greater than 0. Interest can be found by using the following formula:
- [latex]\text{Interest}=FV-N \times PMT[/latex]
In payout annuities and loans problems, [latex]PV[/latex] is the amount that is in the annuity at the start of the annuity or the loan amount, so [latex]PV[/latex] is going to be a number greater than 0. [latex]FV[/latex] will be 0 because the annuity will have no money in it or the loan will be worth $0 in the future. For these problems, interest can be found by using the following formula:
- [latex]\text{Interest}=N \times PMT-PV[/latex]
Let’s take a look at some examples from Sections 4.2-4.5 and see how we would work the same problems using the TVM Solver. Note that the answers to these problems may be a little different than the problems in Sections 4.2-4.5 due to rounding.
Examples from Section 4.2
A traditional individual retirement account (IRA) is a special type of retirement account in which the money you invest is exempt from income taxes until you withdraw it. If you deposit $100 each month into an IRA earning 6% interest, how much will you have in the account after 20 years?
[latex]N = 20 \times 12 = 240[/latex] because you are making monthly