Advanced Algebra with Financial Applications

Advanced Algebra with Financial Applications Formula Sheet

I = Prt  Interest = Principal * rate (as a decimal) * time in years

A = I + P  Account Balance = Interest + Principal

A = Prt + P or A = P (1 + rt)  Account Balance = (Principal * rate * time in years) + Principal Account Balance = Principal * (1 + rate * time in years)

For graphs: y = mx + b (A = Prt + P) m is slope b is y-intercept so m = Pr or r = m/P

Compound Interest Formula A = P(1 + r/n)nt  A = total amount, r = interest rate in decimal form, n = number of times interest is compounded each year, and t = number of years invested

Compound Interest Function A = P(1 + r)t y = abx  y = value after x years, a = original value, b = growth factor, and x = number of years

 This compound interest function is also a special form of a general exponential equation y = abx. The general exponential equation is used often for growth and decay. When the rate r represents growth, b = 1 + r. When it represents decay, b = 1 – r.  The growth or decay factor, b, of an exponential function indicates whether the value will increase or decrease. Exponential growth occurs when b > 1. Exponential decay occurs when 0 < b < 1.

Continuous Change Function A = Pert  Account Balance = Principal * e ^rate * # of periods

 Exponential growth occurs when r > 0. Exponential decay occurs when r < 0.

Balance, with Compound Interest B = P(1 + i)nt  B = balance owed, P = principal, i = periodic interest rate (annual rate r ÷ n), n = number of compounding periods per year, and t = number of years If any payments have been made, subtract the total payments from the calculated balance.

Monthly Payments M = B [ i(1 + i)nt / (1 + i)nt – 1]  M = monthly payment amount, B = balance owed, i = periodic interest rate (annual rate r ÷ n), n = number of compounding periods per year, and t = number of years

Periodic Rate Periodic Rate = APR / # of periods

Annual Percentage Yield APY = (1 + p)n – 1  p = periodic interest rate and n = number of compounding periods

Fixed Rate Mortgage Monthly Payments

 M = monthly payment amount, P = principal, i = periodic interest rate (annual rate r ÷ n), n = number of compounding periods per year, and t = number of years

Remaining Balance of ARM Formula

B is current balance, m is ending month and all other variables are same as fixed rate.

Balance Formula for Balloon Payment

Find the balance after month (m) for Balloon Payment.

Future Value FV = future value FVOA = future value of an ordinary annuity (cash flows at end of each period) FVAD = future value of an annuity due (cash flows at beginning of each period) PV = present value (lump sum) i = periodic interest rate (annual interest rate ÷ number of compounding periods per year) nt = total number of compounding periods (number of compounding periods per year • number of years) C = cash flow (regular payment amount, adjusted to compounding period) Lump Sum FV = PV(1 + i)nt

Ordinary Annuity

Annuity Due

Present Value PV = present value PVOA = present value of an ordinary annuity (cash flows at end of each period) PVAD = present value of an annuity due (cash flows at beginning of each period) FV = future value (lump sum) i = periodic interest rate (annual interest rate ÷ number of compounding periods per year) nt = number of compounding periods (number of compounding periods per year • number of years) C = cash flow (regular payment amount, adjusted to compounding period)

Lump Sum

Ordinary Annuity

Annuity Due

Return on Investment Return on Investment, Dividends