APR, Inflation, Fees, and Loan Borrowing Costs
Summary
The document explores how annual percentage rate relates to nominal and real interest rates, inflation, fees, and the total cost of a loan. It proposes a small calculation that starts with a nominal annual rate, subtracts inflation, then scales the resulting real rate by principal plus fees relative to principal. The author asks whether that formula is sensible for a one-year loan and whether a shorter borrowing period requires annualizing by the number of days.
Its main value is identifying concepts that must be distinguished when interpreting APR: the quoted rate, inflation-adjusted return, fees, loan duration, and repayment amount. The script is presented as a learning aid rather than a validated APR calculation. In particular, it does not resolve how actual lenders calculate APR, how fees are timed, or how compounding and payment schedules affect the rate. The proposed formula also combines real interest with fees in a way that the document leaves open for evaluation, so it should not be treated as a general loan-pricing method.
Key ideas
- APR discussions should distinguish nominal rates, inflation-adjusted rates, fees, and repayment costs.
- The author proposes incorporating total fees by scaling an inflation-adjusted rate against principal.
- The example assumes an annual borrowing period and raises the question of adjusting for shorter durations.
- The script is exploratory and does not establish a standard lender APR calculation.
- Compounding, fee timing, and repayment schedules are not addressed.
Tags
Full text
# Understanding APR via programming
# Understanding APR via programming
I am trying to better understand different types of interest rates. However, I am having difficulties complete, consistent and pedagogically-efficient explanations online. Thus, I have decided to design and program a couple of scripts. I find that programming can be a powerful bridge to truly understand tricky concepts.
The first concept I am trying to understand is the so-called annualized percentage rate (APR). Common explanations basically mention this one as an interest rate that somehow accounts for the costs of the loan...
- The name is very misguiding... right?
- Does it have to be annualized if and only if the given rate is not quoted per annum?
- Also, is it computing using the real interest rate, rather than a nominal interest rate?
- How is the APR used in practice by loan providers? Do they establish a nominal rate that makes sense to them, add the fees and then compute the "APR" to then use it to compute interest payments?
Does the following piece of code make sense? In this piece of code, I use the term "cost-of-borrowing interest rate" to refer to the "APR":
```
inflation_rate_per_year // Annual inflation rate.
nominal_interest_rate_per_year // Nominal interest rate per year.
real_interest_rate_per_year // Inf-adj inf. rate per year.
cost_borrow_interest_rate_per_year // Cost-of-borrowing int. rate.
principal_money // Amount being loaned.
total_fees_money // Total to be payed in fees.
total_cost_loan_money_per_year // Total cost of loan per year.
total_owned_money // Total to pay back.
// Given: inflation_rate_per_year, nominal_interest_rate_per_year
// Given: principal_money, total_fees_money
// Compute real interest rate and percentage.
real_interest_rate_per_year = nominal_interest_rate_per_year - inflation_rate_per_year
// Compute cost-of-borrowing interest rate and percentage.
cost_borrow_interest_rate_per_year =
(total_fees_money + principal_money)/principal_money*
real_interest_rate_per_year
// Compute appreciation on principal.
total_cost_loan_money_per_year =
principal_money*((1 + cost_borrow_interest_rate_per_year) - 1)
total_owned_money = principal_money*(1 + cost_borrow_interest_rate_per_year)
```
Why do I mean by "making sense"? Well, is it OK, considering the given interest rates assume the borrowing period to be 1 year? If it were not a year... Should I have to add the annualization factor of `365/n`, with `n` equaling the number of days in the borrowing period.
I understand the question is posed a little vaguely. I basically want to better understand the APR via this script :)Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.