How to calculate APR including fees

Fees you pay up front mean you receive less than you borrow, but your payment is based on the full amount. The APR is the rate that makes those match.

Problem

A $300,000, 30-year mortgage at 6% comes with $4,500 in fees and points. What is the APR?

Keystrokes

fFINx≷y
0.00
Start clean.
30g12×n
360.00
360 monthly payments.
6g12÷i
0.50
The note rate, monthly.
300000PV
300,000.00
The amount on the note.
PMT
−1,798.65
The payment the lender charges.
RCLPV4500−PV
295,500.00
What you actually receive after fees, stored as the new PV.
i
0.51
The monthly rate that makes the same payment repay that smaller amount.
12×
6.14
The APR.

Answer

With the fees, the APR is 6.14%, against a note rate of 6%.

Why it works

The payment stays fixed at $1,798.65 because the lender bases it on $300,000. But you only walk away with $295,500.00. Solving for i asks: what rate turns $295,500.00 into those 360 payments? That rate is the true cost of the money.

Paying the loan off early

The APR assumes you keep the loan to the end. If you sell or refinance sooner, the fees are spread over fewer payments and the effective cost is higher. To see it, add the remaining balance as FV and change n to the months you expect to keep the loan, then press i again.

Questions

Is APR the same as the effective annual rate?

No. APR is the monthly rate times 12. The effective rate also counts compounding within the year, so it’s a little higher.