Interest

Interest - money paid by a borrower to a lender, beyond the initial amount lent (sometimes called the cost of borrowing money)

Simple interest: I = P x R x T
- I = interest, P = principal amount, R = rate of interest, T = time
- ex; 10,000, 3.1%, 5 years
  - I = 10,000 x .031 × 5
  - I = 1550
- time is based on years. if written as a month, make it a ratio out of 12
  - ex; 5500, 7.3%, 6 months
    - I = 5500 × .073 × 6/12
    - I = 200.75
- Total amount: A= P + I or A = P (I + rt)
  - ex; 10,000, 3.1%, 5 years; whats the total you owe
    - I = 10,000 x .031 × 5
    - I = 1550
    - 10,000 + 1550
    - Total = 11,550
Compound Interest - Interest is paid both on the principal and interest accrued over time
- A = P (1 + r/n)^nt
  - n = compounding rate; how many times the interest on the interest is collected
    - ex; CR = yearly, n = 1. CR = daily, n = 365, CR = quarterly, n = 1
- ex; 1000, 4.5%, 3 years, compound annually
  - 1000 (1 + .045/1)^{1 × 3}
  - 100 (1.045)³
  - = 1,141.17
- Compounding continuously: A = Pe^rt
  - n → ∞
  - e = 2.71
  - ex; 3000, 7.5%, 1 year, compounded continuously
    - 3000 (2.71)^{.075 × 1}
    - = 3,233.65
- Effective Annual Yield - representing how much your investment grows over one year
  - EAY = (1 + r/n)ⁿ- 1
  - ex; 20%, compounded quarterly
    - (1 + .2/4)⁴- 1
    - (1 + .05)⁴- 1
    - (1.05)⁴- 1
    - 1.216 - 1
    - .216
    - EAY = 21.6%