Start with one penny and double it every day. By day 30 you have more than $5 million. That is compounding, and this week you use it to read how fast your own bank is growing.
Learning objectives. After this week you can (1) compute simple interest; (2) compute compound interest and future value; and (3) find the weekly growth rate that connects two bank balances.
Remember this: simple interest is paid on the start. Compound interest is paid on the interest too.
1) Simple interest: rent on money
Interest = Principal × rate × time (I = P × r × t)
Lend $10,000 at 5% simple interest for 3 years: 10,000 × 0.05 × 3 = $1,500. That is the same $500 every year, because simple interest only ever counts the original principal. Time does not have to be whole: $6,000 at 4% for 2.5 years is 6,000 × 0.04 × 2.5 = $600.
Try it
A $10,000 truck loan at 1% a month, held for 3 months.
Interest = Principal × Rate × Time
Fill in the boxes.
2) Compound interest: interest on interest
Future Value = Principal × (1 + r)n
The same $10,000 at 5% compounded yearly for 3 years: 10,000 × 1.05³ = 10,000 × 1.157625 = $11,576.25, which is $76.25 more than simple. Smaller, side by side:
| $5,000 at 5% for 2 years | Balance | Interest |
|---|---|---|
| Simple: 5,000 + 5,000 × 0.05 × 2 | $5,500.00 | $500.00 |
| Compound: 5,000 × 1.05² | $5,512.50 | $512.50 |
The extra $12.50 is 5% interest on the first year's $250 of interest. A handy shortcut, the Rule of 72: money doubles in about 72 ÷ rate years. At 6%, about 12 years; at 9%, about 8.
3) Growth rates: reading your own season
Per-period rate = (End ÷ Start)1/n − 1
Weekly rate from days = (End ÷ Start)7 ÷ days − 1
Run compounding backwards. Your team started with a $50,000 bank. Two weeks in (14 days, so n = 2) it reads $60,500. Total growth is 60,500 ÷ 50,000 = 1.21, and the weekly rate is √1.21 − 1 = 10% per week. Not 10.5%: two 10% weeks make 1.10 × 1.10 = 1.21. Counting in days gives the same answer, because 7 ÷ 14 is the same exponent as 1/2.
Try it
Your bank went from $5,000 to $7,200 over 6 weeks.
Weekly rate % = ((End ÷ Start)1/n − 1) × 100
Fill in the boxes.
4) The cost of idle cash
Interest given up = Idle cash × Annual rate
Your truck's bank pays no interest. If a savings account paid 5% a year, $50,000 sitting idle gives up 50,000 × 0.05 = $2,500 a year, about $7 a day. That is the floor your money could earn somewhere else. Put it next to what one working truck clears in a day.
Quick self-check
(a) Simple interest on $3,000 at 4% for 3 years? (b) $3,000 at 4% compounded yearly for 3 years? (c) Your bank went from $50,000 to $54,080 in 14 days. Weekly compound rate? (Answers: $360; 3,000 × 1.04³ = $3,374.59; √1.0816 − 1 = 4%.)
Common mistakes
- Splitting total growth evenly. 21% over two weeks is 10% a week, not 10.5%.
- Mixing periods. A 5% yearly rate is not 5% a week. Match the rate to the period.
- Counting only the days you opened. The clock runs on days you sat out too.
This week in the arena
Open your day-by-day history. Take your bank at season start, your bank at your latest close, and the day number of that close. Work out your weekly growth rate with (End ÷ Start)7 ÷ days − 1. Is your bank compounding, standing still, or shrinking?