8.5 Multistage Finance Problems
Which equation to use?
When presented with a finance problem (on an exam or in real life), you’re usually not told what type of problem it is or which equation to use or, if you are using Excel, which command to use. The calculator TVM Solver is nice because it is in one location, but it can be difficult to determine what is positive and what is negative. Here are some hints on deciding which equation, command or sign to use based on the wording of the problem.
The easiest types of problem to identify are loans. Loan problems almost always include words like: “loan”, “amortize” (the fancy word for loans), “finance (a car)”, or “mortgage” (a home loan). Look for these words. If they’re there, you’re probably looking at a loan problem. To make sure, see if you’re given what your monthly (or annual) payment is, or if you’re trying to find a monthly payment. Using technology, loans usually have a future value, or FV of 0, PV or the principal of the loan is positive because you are getting the money in your pocket to buy something. The payment is negative because it is money leaving your pocket to the account or loan.
If the problem is not a loan, the next question you want to ask is: “Am I putting money in an account and letting it sit, or am I making regular (monthly/annually/quarterly) payments or withdrawals?” If you’re letting the money sit in the account with nothing but interest changing the balance, then you’re looking at a compound interest problem. The exception would be bonds and other investments where the interest is not reinvested; in those cases you’re looking at simple interest. In compound interest, your present value or PV is negative because you are putting it away from you in the bank. Payment is 0 and FV is positive because you can get that money back to buy something or re-invest it.
If you’re making regular payments or withdrawals, the next questions is: “Am I putting money into the account, or am I pulling money out?” If you’re putting money into the account on a regular basis (monthly/annually/quarterly) then you’re looking at a basic Annuity problem. Basic annuities are when you are saving money. Usually in an annuity problem, your account starts empty, and has money in the future. This means your PV is 0, Payment is negative because you are putting it in and FV is positive.
If you’re pulling money out of the account on a regular basis, then you’re looking at a Payout Annuity problem. In this case, PV is negative, Payments are positive and FV is usually 0, although, you can put a future value in if you would like to end up with a certain amount of money.
Remember, the most important part of answering any kind of question, money or otherwise, is first to correctly identify what the question is really asking, and to determine what approach will best allow you to solve the problem.
Try it Now
For each of the following scenarios, determine if it is a compound interest problem, a savings annuity pr