EXAMPLE 9 Equivalencing to a No-Fee Conventional Loan

In the case of Joe financing your car purchase, we can imagine that you are not borrowing $8470.59 and making an immediate payment of $1270.59, but simply borrowing $7200 and then repaying $7200 as a conventional loan at $235.29 per month over 36 months. The question is, what APR does that amortization correspond to?

We know , , and and need to solve the amortization payment formula for the annual interest rate , which is the APR:

That doesn’t look easy to do! And it isn’t—it cannot be done; it’s algebraically impossible to separate the out by itself. However, you can find the value of by putting the formula into a spreadsheet and trying successive approximations, or else by entering into the spreadsheet. (See Spotlight 21.3, page 888, for details about using a spreadsheet for financial calculations.) You find . Just don’t miss any payments.