Financial Math for Students: NPV, IRR and Interest

Simple vs. compound interest

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Educational estimate based on the data you enter. It doesn't include taxes or future changes. It's not an offer or personalized advice.

NPV and IRR

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Educational estimate based on the data you enter. It doesn't include taxes or future changes. It's not an offer or personalized advice.

Formulas at a glance

Simple interest: A = P · (1 + r · t), where A is the final amount and P the initial capital
Compound interest: A = P · (1 + r)^t, with r the annual rate and t the years
NPV: −Investment + Σ Cash flow_t / (1 + r)^t
IRR: the rate r that makes NPV = 0

Decision rule: if the NPV is positive (or the IRR is higher than your discount rate), the project adds value.

Worked exercises

1. Simple vs. compound

You deposit $1,000 at 10% a year for 3 years. How much do you have with each type of interest?

Simple: 1,000 · (1 + 0.10 · 3) = $1,300
Compound: 1,000 · 1.10^3 = $1,331

Compound gives you $31 more, because each year the interest earns interest too.

2. NPV and IRR

You invest 1,000 and receive 400, 500 and 600 in years 1, 2 and 3. Your discount rate is 10%.

Year 1: 400 / 1.10^1 = 363.64
Year 2: 500 / 1.10^2 = 413.22
Year 3: 600 / 1.10^3 = 450.79

Sum of discounted cash flows = 1,227.65. NPV = 1,227.65 − 1,000 = 227.65. Since it's positive, the project is worth it. The IRR is 21.6%, higher than 10%.