Formulas

Question 1

Reverse Compound Rate

Answer 1

n x [(1 + e)(1 / n) - 1] Ex: Effective rate of 10.52% over 365 compounding periods: 365 x [(1.1052)(1 / 365) - 1] = 0.10 = 10%

Question 2

Future Value (Single Period)

Answer 2

PV + (PV x r)

Ex: Over the course of one year, a $1 investment grows to $1 + ($1 x r), which equals $1 x (1 + r). In other words, the future value in one year of $1 today is $1 x (1 + r).

Question 3

Future Value (Multiple/Compounded Period)

Answer 3

FV_n = PV x (1 + r)ⁿ.

EX: The future value in two years of $1 today, FV2, is the future value in one year, FV1, increased to reflect the r return in the second year, so that:

FV2 = FV1 + (FV1 x r) = FV1 x (1 + r).

So, if FV1 = $1 x (1 + r), then FV2 = FV1 x (1 + r) = [$1 x (1 + r)] x (1 + r) = $1 x (1 + r).

Question 4

Present Value

Answer 4

PV (FV_n) = FV_n÷(1 + r)ⁿ

Ex 1: If r = 0.1 (10%), what is the present value of $1.10 to be paid one year from now?

PV₁ ($1.10) = $1.10 ÷ (1 + 0.1) = $1

Ex 2: What is the present value at 10% of $1,331 three years from now?

PV₃ ($1,331) = $1,331 ÷ (1.1)³ = $1,331 ÷ 1.331 = $1,000

Question 5

Annuity Analysis

Answer 5

Annuity that pays at the end of each period:

PV = [PMT x 1 - (1 ÷ (1 + r)ⁿ)] ÷ r

Annuity that pays at the beginning of each period:

PV = PMT x (1 + r) x [1 - (1 ÷ (1 + r)ⁿ) ÷ r]

Question 6

Annuity Payments

Answer 6

PMT = PV x (r ÷ [PMT x 1 - (1 ÷ (1 + r)ⁿ)])