US APR family
| Time Value Of Money Analysis category | Home |
| Component | What the name means |
|---|---|
| APRToQuoted | Convert a US style APR to a quoted interest rate |
| QuotedToAPR | Convert a quoted simple annual interest rate to a US style APR |
This family converts a quoted interest rate to a US-style APR, taking into account fees.
The procedure for adjusting a quoted rate to an APR is:
- Add the fees to the loan advance.
- Compute the annual payment required to amortise the loan, taking into account the payment frequency (5 years of monthly payments=60 payments).
- Solve the relation: LoanAmount - Present Value of Loan Repayments = 0, where the interest rate for the calculation of the present value is iteratively derived. This interest rate is the APR.
So what the calculation does is work out the IRR (Internal Rate Of Return) of the loan - but with one important difference. Whilst the cashflow on day 1 is the loan amount, the repayments are based on the loan amount plus the fees.
The method does not produced an annually compounded rate. Usually, the input quoted rate is a simple interest rate, applied monthly. The resultant APR is also a simple interest rate, applied monthly - it's just that it takes into account the fees.
See the notes under each function for the actual equations (and their derivations) used.
Note that both the QuotedRate and the USAPR are simple interest rates, not annually compounded rates (in the UK, the APR is an annually compounded rate). What the APR process simply does is adjust the quoted rate for the fees.