A $100,000 loan at 6% costs about $16 a day, less than one lift ticket. Whether that is cheap depends on what the money earns, and on what inflation is doing behind your back.
Learning objectives. After this week you can (1) compute simple and daily interest; (2) find the real interest rate; and (3) explain how a credit rating and a central bank move the cost of borrowing.
Remember this: real interest rate ≈ nominal rate − inflation. That is what a loan really costs.
1) The price of money
The interest rate is the price of borrowing. The principal is the amount borrowed.
Interest = Principal × Rate × Time
A $10,000 loan at 8% for one year costs 10,000 × 0.08 = $800. A $50,000 lift financed at 8% costs $4,000 a year.
2) Daily interest, and reading your own rate
Daily Interest = Balance × Annual Rate ÷ 365
Your Daily Report shows your Loan balance and the interest charged per day. Turn the formula around and you can find the annual rate you are paying: rate = daily interest × 365 ÷ balance. A $50,000 balance charged $16.44 a day is 16.44 × 365 ÷ 50,000 = 12% a year. Interest is charged every day, whether or not anyone skis.
3) Real vs. nominal interest
A 7% loan during 3% inflation has a real rate of about 4%: the dollars you repay are worth less than the ones you borrowed. A 9% loan during 4% inflation is about 5% real. If inflation (4%) beats the loan's rate (3%), the real rate is negative (−1%): inflation is quietly paying part of the loan.
4) Credit ratings and central banks
Your credit rating is your borrowing reputation, and it is on your Daily Report. A higher rating earns a lower rate; missed payments and shaky finances lower it and raise what you pay later. For the whole economy, the central bank sets a key policy rate: it raises rates to cool inflation and lowers them to encourage borrowing and spending. Higher rates slow borrowing and investment.
Quick self-check
(a) A $15,000 loan at 5% for one year. Interest? (b) A $20,000 balance is charged $5.48 a day. Annual rate? (c) Nominal rate 6%, inflation 2%. Real rate? (Answers: $750; 5.48 × 365 ÷ 20,000 ≈ 10%; about 4%.)
Common mistakes
- Using the annual rate as a daily one. Divide by 365 for a day's interest.
- Judging a loan by its sticker rate. Subtract inflation to see the real cost.
- Treating interest as optional. It accrues on bad days exactly as on good ones.
This week in the arena
If your resort carries a loan, read the balance and the interest per day off one report and work out the annual rate you are paying. Then check your credit rating on the same report. No loan yet? Work the daily interest on $50,000 at 6% and compare with a classmate who does borrow.