MATH 034 Formulas Simple Interest Formula I = .docx
- 1. MATH 034 Formulas Simple Interest Formula I = PRT I = simple interest P = principal R = simple interest rate T= term Nth Term of An Arithmetic Sequence an = a1 + (n – 1)d a1 = first term d = common difference Sum of the First n Terms of an Arithmetic Sequence Sn = (n/2)(a1 + an) a1 = first term an = nth term
- 2. Simple Discount Formula D = MdT D = simple discount M = maturity value d = simple discount rate T = term Compound Interest Formula FV = PV(1 + i) n FV = future value PV = present value i = interest rate per compounding period n = number of compounding periods N+1 st Term of a Geometric Sequence an = a0 r n a0 = first term a1 = second term
- 3. r = common ratio = a1/a0 Sum of the First n Terms of a Geometric Sequence Sn = a0 (1 – r n ) / (1 – r) a0 = first term r = common ratio = a1/a0 Infinite Geometric Sum S∞ = a0 /(1 – r) a0 = first term r = common ratio = a1/a0 Compound Interest Rate i = compound interest rate FV = future value PV = present value n = number of compounding periods
- 4. Time Periods n = log (FV/PV) log (1 + i) i = compound interest rate FV = future value PV = present value Rule of 72 The time required for a sum of money to double at a compound interest rate of x% is approximately 72/x years. (x should not be converted to a decimal) Rule of 72 (Alternate Form) The compound interest rate required for a sum of money to double in x years is approximately 72/x percent.
- 5. Effective Interest Rate Eff. Rate = (1 + r/c) c – 1 r = the nominal interest rate c = the number of compoundings per year Continuous Compounding FV = PV e (rt) FV = future value PV = present value e = a mathematical constant (approx. 2.71828) r = annual interest rate t = number of years Future Value Annuity Factor sn/i = i = interest rate per payment period n = number of payment periods Future Value of an Ordinary Annuity FV = PMTsn/i FV = future value of the annuity
- 6. PMT = amount of each payment sn/i = annuity factor Future Value of an Annuity Due FV = PMTsn/i(1 + i) FV = future value of the annuity PMT = amount of each payment i = interest rate per payment period sn/i = annuity factor Interest for Future Value Annuities interest = FV – total deposits Present Value Annuity Factor i = interest rate per payment period n = number of payment periods Present Value of an Ordinary Annuity PV = PMTan/i PV = present value of the annuity PMT = amount of each payment an/i = present value annuity factor
- 7. Present Value of an Annuity Due PV = PMTan/i(1 + i) PV = present value of the annuity PMT = amount of each payment an/i = present value annuity factor Interest for Present Value Annuities interest = total deposits – PV 1/ ( ) 1 nFV i PV i i n i
- 8. i a n in )1(1 / Sales Tax T = P(1 + r) T = total price including tax P = price before tax r = sales tax rate T – P = amount of tax Income Tax Formulas Annual taxable income = annual income – benefits – exemptions – deductions
- 9. Paycheck taxable income = paycheck income – benefits – exemptions FICA taxes based on paycheck income – benefits Dividends dividend per share = total dividend total # shares individual dividend = (dividend per share)(# individual shares) current dividend yield = quarterly dividend per share × 4 market price per share trailing divided yield = trailing dividend per share market price per share Compound Annual Growth Rate or Rate of Return
- 10. i = compound growth rate FV = future value PV = present value n = number of years Net Asset Value (NAV) NAV = total assets / total number of shares Mutual Fund Shares # shares = amount invested / NAV Inflation Formula FV = PV(1 + i) n FV = future value of an item PV = present value of an item i = rate of inflation n = number of time periods Declining Balance Depreciation FV = PV(1 + i) n
- 11. FV = future value PV = present value i = depreciation rate n = years Straight Line Depreciation Total depreciation amount = Original value – Residual value Annual depreciation = Total depreciation amount Useful Life Depreciated value = Original value – (# of years)(Annual depreciation) Credit Card Interest I = PRT I = interest P = principal R = interest rate
- 12. T= term Mortgage Formulas Equity = value of home – amount of mortgage Total PITI = principal + interest + taxes + insurance(s) One point = 1% of the amount of the loan Payback period = cost of points / monthly savings The 28% Rule Total PITI cannot exceed 28% of gross monthly income. The 36% Rule Total PITI and all other long-term debt payments cannot exceed 36% of gross monthly income. Lease Payment = Payment on Loss + Interest on Residual Payment on loss: Use PV = PMTan/i where PV = original price – residual value Interest on residual: Use I=PRT where P = residual value
- 13. Markup Based on Cost P = C(1 + r) P = selling price C = cost r = percent markup Markup Based on Selling Price C=SP(1 – r) C = item’s cost SP = selling price r = gross profit margin Markdown MP = OP(1 – d) MP = marked-down price OP = original price d = percent markdown Profit Margin Formulas Gross profit = sales – cost Gross profit margin = gross profit / sales
- 14. Gross profit = (gross profit margin)(sales) Net profit = sales – cost – expenses Net profit margin = net profit / sales Cost-Revenue Analysis P = R – C P = profit function R = revenue function C= cost function 1/ ( ) 1 nFV i PV