Lesson 3 of 25 · 7 min

APR, and what is inside it

Fees packed into the principal change the rate that actually describes the cash, not the contract rate on the paper.

APR, the annual percentage rate, restates interest plus certain financed fees as one annual figure. The contract rate on the paper is a different input. When fees are added to the principal, the cash you receive is smaller than the cash you repay, and APR is the rate that describes that gap as a year.

Cinderwell Dealer writes $24,180 at a 6.1 percent contract rate, then finances $895 of fees on top, so the principal the installment is computed on is $24,180 + $895 = $25,075. The APR that corresponds to that structure, illustrative, is 7.24 percent. Two different substitutions now exist, and they do not produce the same month.

Payment on $25,075 at 7.24 percent for 48 months is $603.25. The total of those payments is $28,955.91. Payment on the $24,180 of car at the 6.1 percent contract rate for the same 48 months would be $568.98, totalling $27,310.91. The $1,645.00 gap between those totals is the fees plus the interest the fees themselves accrue. The 6.1 percent figure never saw the $895.

Track 1 lesson 15 is the day-count version of the same move: a posted rate becomes a different year once a convention is applied. This lesson does not re-open Act/360. APR is that move for fees. A contract rate describes interest on a named principal. APR describes the cash schedule that actually leaves the account, after the fees have been folded in.

Two rates can sit on the same page. The lower one is the contract rate on the car. The higher one is the year that describes the cash, fees included.

Key terms

Contract rate: The interest rate written on the principal of the loan, before financed fees are restated as a year.
APR (annual percentage rate): A restatement of interest plus certain financed fees as one annual rate on the cash that actually moved.
Financed fee: A charge added to the principal so that it is paid, with interest, over the term.

Worked example

One car, two substitutions

Cinderwell Dealer. Amount $24,180 at a 6.1 percent contract rate. $895 of fees financed. 48 months. Illustrative APR 7.24 percent.

Principal the installment uses: $25,075
Payment on $25,075 at 7.24%: $603.25
Total at 7.24%: $28,955.91
Payment on $24,180 at 6.1%: $568.98
Total at 6.1%: $27,310.91
Gap between totals: $1,645.00

The 6.1 percent rate is true of $24,180. The 7.24 percent APR is true of the cash schedule. They are not two names for one number.

Check yourself

A loan of $19,250 at a 5.5 percent contract rate finances $640 of fees, so the principal is $19,890. Illustrative APR 6.8 percent, 36 months. What are the two monthly payments, and what are the two totals?

APR restates several charges as one annual rate, the same move Track 1 lesson 15 makes when a day-count convention turns a posted rate into a different year. Open Act/360, and why the day count matters →

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Educational only. Nothing in this lesson is investment, legal or tax advice, or a recommendation to enter into any transaction. Figures are illustrative and computed from the inputs stated in the lesson.