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Queuing and Waiting Theory, Graduated Payment Mortgage, Average number of customers in queue.

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Queuing and Waiting Theory • n = number of servers. • λ = arrival rate of customers (Poisson input). • µ = service rate for each server (exponential service). • ρ = Intensity factor n for valid results). • P0 = Probability that all servers are idle. • Pb = Probability that all servers are busy. • Lq = Average number of customers in queue. • L = Average number of customers in the system (waiting and being served). • Tq = Average waiting time in queue. • T = Average total time through the sytem. • P(t) = Probability of waiting longer than time t. • P0 = -1 n-1 ∑k = 0 -ρk---!k- + n---------- n!   1 - n-ρ- • Pb = ------ρ---n---P-----0-----n!1 - n-ρ- • • Lq = -n-ρ---P-----b-ρ-- L = Lq + ρ T = L / λ Tq = L--λ--q- • P(t) = Pbe-(nµ - λ)t Graduated Payment Mortgage 163

Section	Page
Introduction	2
Real Estate	3
Refinancing	3
Wrap-Around Mortgage	4
Income Property Cash Flow Analysis	8
a. What is the Effective Gross Income?	8
b. What is the Net Operating Income?	8
c. What is the Cash Throw-Off to Equity?	8
Lending	21
Loan With a Constant Amount Paid Towards Principal	21
Add-On Interest Rate Converted to APR	22
APR Converted to Add-On Interest Rate.	23
a. Key in number of months of loan and press .	23
b. Key in APR and press .	23
c. Key in 100 and press .	23
Add-On Rate Loan with Credit Life.	24
Interest Rebate - Rule of 78's	28
Graduated Payment Mortgages	30
a. The current year. Then press to continue.	34
b. The monthly payment for the current year. Then press to continue.	34
c. The remaining balance to be paid on the loan at the end of the current year. Then press to ret...	34
Variable Rate Mortgages	35
a. Key in the previous remaining balance. If this is the first mortgage adjustment, this value is...	36
b. Key in the annual interest rate before the adjustment (as a percentage) and press .	36
c. Key in the number of years since the last adjustment. If this is the first mortgage adjustment...	36
d. Key in the monthly payment over this period and press .	36
e. Press to find the remaining balance, then press CLEAR .	36
a. Key in the remaining life of the mortgage (years) and press .	36
b. Press to find the new monthly payment.	36
c. Key in the present monthly payment and press .	36
d. Press 12 to find the remaining term of the mortgage in years.	36
Skipped Payments	37
Savings	39
Initial Deposit with Periodic Deposits	39
Number of Periods to Deplete a Savings Account or to Reach a Specified Balance.	40
Periodic Deposits and Withdrawals	40
Savings Account Compounded Daily	42
Compounding Periods Different From Payment Periods	45
Investment Analysis	48
Lease vs. Purchase	48
Break-Even Analysis	53
a. Key in the fixed costs, F and press 1.	57
b. Key in the variable costs per unit, V and press 2.	57
c. Key in the unit price, P (if known) and press 3.	57
d. Key in the sales volume, U, in units (if known) and press 4.	57
e. Key in the gross profit, GP, (if known) and press 5.	57
a. Store values as shown in 1a, 1b, and 1c.	57
b. Key in the desired gross profit (zero for break even) and press 5.	57
c. Press 10 to calculate the required volume.	57
a. Store values as shown in 1a, 1b, 1c, and 1d.	57
b. Press 05 to calculate gross profit.	57
a. Store values as shown in 1a, 1b, 1d, and 1e.	57
b. Press 16 to calculate the required sales price.	57
Operating Leverage	58
Profit and Loss Analysis	60
a. Key in the list price in dollars (if known) and press 1.	63
b. Key in the discount in percent (if known) and press 2.	63
c. Key in the manufacturing cost in dollars (if known) and press 3.	63
d. Key in the operating expense in percent (if known) and press 4.	63
e. Key in the net profit after tax in percent (if known) and press 5.	63
a. Do steps 2 and 3b, c, d, e above.	63
b. Press 3 1 14 00.	63
a. Do steps 2 and 3a, c, d, e above.	63
b. Press 3 29 .	63
a. Do steps 2 and 3a, b, d, e, above.	63
b. Press 13 01 .	63
a. Do steps 2 and 3a, b, c, e, above.	63
b. Press 12 38 .	63
a. Do steps 2 and 3a, b, c, d, above.	63
b. Press 12 43 .	64
Securities	66
After-Tax Yield	66
Discounted Notes	68
a. Key in the discount rate and press 5.	70
b. Press to calculate the purchase price.	70
c. Press to calculate the yield.	70
d. For a new case, go to step 3.	70
a. Key in the price and press 5.	70
b. Press 15 to calculate the yield.	70
c. For a new case, go to step 3.	70
Forecasting	72
Simple Moving Average	72
Seasonal Variation Factors Based on Centered Moving Averages.	77
a. Key in 1st quarter sales and press 1.	78
b. Key in 2nd quarter sales and press 2.	79
c. Key in 3rd quarter sales and press 3.	79
d. Key in 4th quarter sales and press 4.	79
e. Key in the 1st quarter sales for the next year and press 5.	79
Gompertz Curve Trend Analysis	83
Forecasting with Exponential Smoothing	88
Pricing Calculations	94
Markup and Margin Calculations	94
Calculations of List and Net prices With Discounts	96
Statistics	100
Curve Fitting	100
Standard Error of the Mean	107
Mean, Standard Deviation, Standard Error for Grouped Data	108
Chi-Square Statistics	111
Normal Distribution	114
Covariance	118
Permutation	120
Combination	122
Random Number Generator	123
Personal Finance	125
Homeowners Monthly Payment Estimator	125
Tax-Free Individual Retirement (IRA) of Keogh Plan.	128
Stock Portfolio Evaluation and Analysis	131
Canadian Mortgages	137
Periodic Payment Amount	137
Number of Periodic Payments to Fully Amortize a Mortgage	138
Effective Interest Rate (Yield)	138
Balance Remaining at End of Specified Period	138
Miscellaneous	140
Learning Curve for Manufacturing Costs	140
a. Key in C1, the cost of the first unit and press .	143
b. Key in Cn, the cost of the nth unit and press .	143
c. Key in n, the number of units and press to calculate r the learning factor.	143
a. Key in C1 and press 1. Key in r and press 2. (Note: This step may be skipped if step 2 has jus...	143
b. Key in the number of units, n and calculate Cn, the cost of the nth unit by pressing 16 .	143
a. Key in C1 and press 1. Key in r and press 2. (Note: This step may be skipped if step 2 has jus...	143
b. Key in the number of the last unit of the batch, j and press .	143
c. Key in the number of the first unit of the batch, i, and calculate the average cost per unit b...	143
Queuing and Waiting Theory	144
Appendix	151
Real Estate	151
Lending	152
Savings	153
Investment Analysis	154
Securities	155
Forecasting	155
Pricing Calculations	158
Statistics	160
Personal Finance	162
Canadian Mortgages	163