Real APR of a loan with fees and insurance
The real APR is the annual rate that equates what you receive (the principal minus upfront costs) with the present value of what you pay (instalments plus tied insurance). For 20,000 € at 7% over 5 years, with a 1% opening fee and 45 € a month of insurance, the real APR is 12.75% and the total outlay is 26,661.44 €.
received = Σ (payment + insurance) / (1 + j)^k → APR = (1 + j)^12 − 1
Updated: · Albea Systems
Result
Yearly schedule
| Year | Payment | Interest | Principal | Balance |
|---|---|---|---|---|
| 1 | €4,752 | €1,290 | €3,462 | €16,538 |
| 2 | €4,752 | €1,040 | €3,712 | €12,826 |
| 3 | €4,752 | €772 | €3,981 | €8,845 |
| 4 | €4,752 | €484 | €4,268 | €4,577 |
| 5 | €4,752 | €175 | €4,577 | €0 |
How it is calculated
The calculation finds the monthly rate j at which the present value of all the payments equals what you actually receive: the principal minus the upfront costs. It is then annualised as (1 + j)^12 − 1. Capital solves it by bisection, which cannot diverge or land on a wrong root.
Insurance counts when taking it out is a condition of the offer. If you can buy the insurance yourself and it is cheaper, compare the two options separately.
Capital does this calculation on your device, with the same figures you see here.
Download on the App StoreFrequently asked questions
Which costs go into the real APR?
The opening fee, the appraisal, the paperwork and notary you pay at signing, and the instalments of tied insurance. Capital lets you enter each one separately.
Why is my APR higher than the one my bank gives me?
It can be if you include costs the bank’s sheet leaves out of its APR, or insurance the bank treats as optional. Ask for the offer in writing and compare item by item.
How much does a tied insurance and a fee add to the APR?
It depends on the amount and the term. In the example, a 1% fee and 45 € a month of insurance (2,700 € over 5 years) take the APR from 7.23% to 12.75%.
More calculators
- Nominal rate vs APRWhat each one counts, and how far apart they get in a real example.
- Loan paymentMonthly payment, interest and total paid under all three systems.
- Early repaymentReduce term or payment, with cancellation fee and against investing.
- French, linear and AmericanThe three systems with your numbers: payment, interest and balance.
- Amortization schedulePayment, interest, principal and balance every month and every year.
- Compare two loansReal APR, payment and total outlay of two offers side by side.
- Deposit: net interestGross interest, tax, fees, inflation and net return.
- Download on the App StoreCapital does this calculation on your device, with the same figures you see here.