Simple & Compound Interest – Quick Study Notes
Designed for the quantitative‑aptitude section of the AWS Certification exam.
📌 1. Simple Explanation
| Concept | What it is | How it works |
|---|---|---|
| Simple Interest (SI) | Interest calculated only on the principal amount each period. | SI = P × r × t |
| Compound Interest (CI) | Interest calculated on principal + accumulated interest. | A = P × (1 + r/n)^(n·t) (n = compounding frequency) |
- P – Principal (initial amount)
- r – Annual interest rate (as decimal, e.g. 8% → 0.08)
- t – Time in years
- n – Number of compounding periods per year
- A – Amount after t years (principal + interest)
Why it matters
- In cloud‑finance models (e.g., on‑demand vs. reserved instances) understanding how costs compound over time is crucial.
- AWS pricing often involves discounts that are effectively compound interest on future spend.
📚 2. Key Points
| Topic | Key Take‑aways |
|---|---|
| Simple Interest | • Linear growth. • Formula: SI = P × r × t.• No compounding → easier mental math. |
| Compound Interest | • Exponential growth. • Formula: A = P × (1 + r/n)^(n·t).• Common in loans, savings, and AWS reserved‑instance pricing. |
| Compounding Frequency | • Daily, monthly, quarterly, yearly. • More frequent compounding → higher effective rate. |
| Effective Annual Rate (EAR) | EAR = (1 + r/n)^n – 1.• Converts nominal rate to actual yearly return. |
| Continuous Compounding | A = P × e^(r·t).• Rare in AWS pricing but useful for theoretical problems. |
| Solving for Unknowns | • If 2 of 3 variables (P, r, t) known → isolate the unknown. • Use logarithms for CI when solving for t or r. |
| Common AWS‑Related Problems | • Calculating total cost of an R‑instance over 3 years with a 15% discount per year (compound effect). • Determining break‑even time for a savings plan with simple interest. |
🚀 3. Worked Example
Problem
You invest $5,000 in a savings account that pays 8 % p.a. compounded quarterly.
- What will be the amount after 5 years?
- What is the simple interest earned over the same period?
- What would be the effective annual rate (EAR)?
1. Compound Interest – Amount After 5 Years
| Variable | Value |
|---|---|
| P | 5,000 |
| r | 0.08 (8 %) |
| n | 4 (quarterly) |
| t | 5 |
Formula
A = P × (1 + r/n)^(n·t)
Calculation
A = 5,000 × (1 + 0.08/4)^(4×5)
= 5,000 × (1 + 0.02)^(20)
= 5,000 × 1.02^20
Compute 1.02^20 (use a calculator or log table):
1.02^20 ≈ 1.485947
A ≈ 5,000 × 1.485947 = $7,429.74
Answer: $7,429.74 after 5 years.
2. Simple Interest Earned Over 5 Years
SI = P × r × t = 5,000 × 0.08 × 5 = 5,000 × 0.4 = $2,000
Answer: $2,000 simple interest.
3. Effective Annual Rate (EAR)
EAR = (1 + r/n)^n – 1 = (1 + 0.08/4)^4 – 1
EAR = (1 + 0.02)^4 – 1
= 1.02^4 – 1
= 1.08243216 – 1
= 0.08243216 ≈ 8.24%
Answer: EAR ≈ 8.24 % per year.
Quick Mental Math Tricks (for AWS exam)
- Quarterly compounding: Multiply by 1.02 each quarter.
After 4 quarters (1 year):1.02^4 ≈ 1.082.
After 2 years:1.082^2 ≈ 1.171. - SI easy:
P × r × t→ just multiply two numbers then the third.
📝 4. Quick Revision Summary
| Concept | Formula | Typical AWS Context |
|---|---|---|
| Simple Interest | SI = P × r × t |
Calculating cost of pay‑as‑you‑go over a fixed period. |
| Compound Interest | `A = P × (1 + r/n)^(n |