Explanation Given Information: In a saving account, $ 1000 are deposited paying 3 % interest compounded annually and $ 150 is added to the account at the end of each year. Formula used: The balance at the beginning of the next year can be calculated as, [ balance at the beginning of the next year ] = [ balance at the beginning of the previous year ] + [ interest on balance for previous year ] + [ amount added at the end of the previous year ] Calculation: The balances in the account for the first few years can be determined by the above details in the following chart, where y 0 is the initial balance and y 1 is the balance after one year of deposition and y 2 is the balance after two year of deposition and y 3 is the balance after three year of deposition. The table is showing the balance after each year with the addition of interest per year. Year Balance Interest for year Amount added 0 y 0 = $ 1000 ( 0.03 ) 1000 = $ 30.00 $ 150 1 y 1 = $ 1180.00 ( 0.03 ) 1180.00 = $ 35.4 $ 150 2 y 2 = $ 1365.4 ( 0.03 ) 1365.4 = $ 40.962 $ 150 3 y 3 = $ 1556.362 The interest for the first year will be interest rate multiply by the balance of the initial year with the addition of interest of previous year and the amount added at the end of the previous year as shown, ( 0.03 ) [ 1000 + 30.00 + 150 ] = $ 35.4 ( 0.03 ) 1180.00 = $ 35.4 Once the balance is known for the beginning of the particular year, the balance at the beginning of the next year is computed as follows: [ balance at the beginning of the next year ] = [ balance at the beginning of the previous year ] + [ interest on balance for previous year ] + [ amount added at the end of the previous year ] Hence, y 1 = y 0 + 0.03 y 0 + 150 y 2 = y 1 + 0

Finite Mathematics & Its Applications (12th Edition)

12th Edition

ISBN: 9780134507125

Author: Goldstein

Publisher: PEARSON

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Chapter 12.1, Problem 18E

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To calculate: The difference equation computing yn from yn−1 when $1000 are deposited into a savings account paying 3% interest compounded annually and at the end of each year, $150 is added to the account. The value of yn is the amount after n years.

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Chapter 12.1, Problem 17E

Chapter 12.1, Problem 19E

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Chapter 12 Solutions

Finite Mathematics & Its Applications (12th Edition)

Ch. 12.1 - Consider the difference equation...Ch. 12.1 - Prob. 2CYU Ch. 12.1 - Prob. 1E Ch. 12.1 - Prob. 2E Ch. 12.1 - Prob. 3E Ch. 12.1 - Prob. 4E Ch. 12.1 - Prob. 5E Ch. 12.1 - For each of the difference equations in Exercises...Ch. 12.1 - Prob. 7E Ch. 12.1 - Prob. 8E

Ch. 12.1 - Prob. 9E Ch. 12.1 - Prob. 10E Ch. 12.1 - Prob. 11E Ch. 12.1 - Prob. 12E Ch. 12.1 - Prob. 13E Ch. 12.1 - Prob. 14E Ch. 12.1 - Prob. 15E Ch. 12.1 - Prob. 16E Ch. 12.1 - Prob. 17E Ch. 12.1 - Prob. 18E Ch. 12.1 - Prob. 19E Ch. 12.1 - Population Decline Moldova has negative population...Ch. 12.1 - Prob. 21E Ch. 12.1 - Prob. 22E Ch. 12.1 - Prob. 23E Ch. 12.1 - Prob. 24E Ch. 12.1 - Prob. 25E Ch. 12.1 - Prob. 26E Ch. 12.1 - 27. Credit Card Mr. Jones owes $1000 on a credit...Ch. 12.1 - Prob. 28E Ch. 12.1 - Prob. 29E Ch. 12.1 - Prob. 30E Ch. 12.1 - Prob. 31E Ch. 12.1 - Prob. 32E Ch. 12.1 - Prob. 33E Ch. 12.1 - Prob. 34E Ch. 12.1 - Prob. 35E Ch. 12.2 - Prob. 1CYU Ch. 12.2 - Prob. 2CYU Ch. 12.2 - Prob. 1E Ch. 12.2 - Prob. 2E Ch. 12.2 - Prob. 3E Ch. 12.2 - Prob. 4E Ch. 12.2 - Prob. 5E Ch. 12.2 - Prob. 6E Ch. 12.2 - Prob. 7E Ch. 12.2 - Prob. 8E Ch. 12.2 - Prob. 9E Ch. 12.2 - Prob. 10E Ch. 12.2 - Prob. 11E Ch. 12.2 - Prob. 12E Ch. 12.2 - Prob. 13E Ch. 12.2 - Prob. 14E Ch. 12.2 - Prob. 15E Ch. 12.2 - Prob. 16E Ch. 12.2 - Prob. 17E Ch. 12.2 - Prob. 18E Ch. 12.2 - Prob. 19E Ch. 12.2 - Prob. 20E Ch. 12.2 - Prob. 21E Ch. 12.2 - Prob. 22E Ch. 12.2 - Prob. 23E Ch. 12.2 - Prob. 24E Ch. 12.2 - Prob. 25E Ch. 12.2 - Prob. 26E Ch. 12.2 - Prob. 27E Ch. 12.2 - Prob. 28E Ch. 12.3 - Parachuting A parachutist opens her parachute...Ch. 12.3 - Prob. 2CYU Ch. 12.3 - 3. Retirement Fund Upon retirement, a person...Ch. 12.3 - Each of the graphs in Fig. 14 comes from a...Ch. 12.3 - Prob. 2E Ch. 12.3 - Prob. 3E Ch. 12.3 - Prob. 4E Ch. 12.3 - Each of the graphs in Fig. 14 comes from a...Ch. 12.3 - Prob. 6E Ch. 12.3 - Each of the graphs in Fig. 14 comes from a...Ch. 12.3 - Prob. 8E Ch. 12.3 - In Exercises 914, sketch a graph having the given...Ch. 12.3 - Prob. 10E Ch. 12.3 - In Exercises 914, sketch a graph having the given...Ch. 12.3 - Prob. 12E Ch. 12.3 - Prob. 13E Ch. 12.3 - Prob. 14E Ch. 12.3 - Prob. 15E Ch. 12.3 - Prob. 16E Ch. 12.3 - Prob. 17E Ch. 12.3 - Prob. 18E Ch. 12.3 - Prob. 19E Ch. 12.3 - Prob. 20E Ch. 12.3 - Prob. 21E Ch. 12.3 - Prob. 22E Ch. 12.3 - Prob. 23E Ch. 12.3 - Prob. 24E Ch. 12.3 - Prob. 25E Ch. 12.3 - Prob. 26E Ch. 12.3 - Prob. 27E Ch. 12.3 - Prob. 28E Ch. 12.3 - Prob. 29E Ch. 12.3 - Prob. 30E Ch. 12.3 - Prob. 31E Ch. 12.3 - Prob. 32E Ch. 12.3 - In these exercises, find a difference equation...Ch. 12.3 - Prob. 34E Ch. 12.3 - Prob. 35E Ch. 12.3 - Prob. 36E Ch. 12.4 - Prob. 1CYU Ch. 12.4 - Prob. 2CYU Ch. 12.4 - Prob. 3CYU Ch. 12.4 - Prob. 1E Ch. 12.4 - Prob. 2E Ch. 12.4 - Prob. 3E Ch. 12.4 - Prob. 4E Ch. 12.4 - Prob. 5E Ch. 12.4 - 6. Find the monthly payment on a 25-year $38,000...Ch. 12.4 - Prob. 7E Ch. 12.4 - Prob. 8E Ch. 12.4 - Prob. 9E Ch. 12.4 - Prob. 10E Ch. 12.4 - Prob. 11E Ch. 12.4 - Prob. 12E Ch. 12.4 - Prob. 13E Ch. 12.4 - In these exercises, use a table or graph of an...Ch. 12.4 - In these exercises, use a table or graph of an...Ch. 12.4 - Prob. 16E Ch. 12.5 - Glucose Infusion Glucose is being given to a...Ch. 12.5 - Light at Ocean Depths Sunlight is absorbed by...Ch. 12.5 - 1. Population Dynamics In a certain country with...Ch. 12.5 - Population Dynamics A small city with current...Ch. 12.5 - 3. Drug Absorption After a certain drug is...Ch. 12.5 - Elevation and Atmospheric Pressure The atmospheric...Ch. 12.5 - Spread of Information A sociological study was...Ch. 12.5 - Solution Concentration A cell is put into a fluid...Ch. 12.5 - Learning Curve Psychologists have found that in...Ch. 12.5 - Genetics Consider two genes A and a in a...Ch. 12.5 - Account Balance Thirty thousand dollars is...Ch. 12.5 - 10. Account Balance Rework Exercise 9, where...Ch. 12.5 - Prob. 11E Ch. 12.5 - Prob. 12E Ch. 12.5 - Prob. 13E Ch. 12.5 - Prob. 14E Ch. 12.5 - Prob. 15E Ch. 12.5 - Prob. 16E Ch. 12.5 - Prob. 17E Ch. 12.5 - Prob. 18E Ch. 12.5 - In these exercises, answer the questions by...Ch. 12.5 - Prob. 20E Ch. 12 - Explain how a sequence of numbers is generated by...Ch. 12 - Prob. 2FCCE Ch. 12 - Prob. 3FCCE Ch. 12 - Prob. 4FCCE Ch. 12 - Prob. 5FCCE Ch. 12 - Prob. 6FCCE Ch. 12 - Prob. 7FCCE Ch. 12 - Prob. 8FCCE Ch. 12 - Prob. 9FCCE Ch. 12 - Prob. 10FCCE Ch. 12 - Prob. 1RE Ch. 12 - Prob. 2RE Ch. 12 - 3. Account Balance How much money would you have...Ch. 12 - Prob. 4RE Ch. 12 - Prob. 5RE Ch. 12 - Prob. 6RE Ch. 12 - Population Dynamics The population of a certain...Ch. 12 - 8. Mortgage The monthly payment on a 30-year...Ch. 12 - Prob. 9RE Ch. 12 - Prob. 10RE Ch. 12 - Prob. 11RE Ch. 12 - Prob. 12RE Ch. 12 - Prob. 13RE Ch. 12 - Prob. 14RE Ch. 12 - Prob. 1P Ch. 12 - Prob. 2P Ch. 12 - Prob. 3P Ch. 12 - Prob. 4P Ch. 12 - Prob. 5P Ch. 12 - Prob. 6P Ch. 12 - Prob. 7P Ch. 12 - Prob. 8P Ch. 12 - Prob. 9P

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The difference equation computing y n from y n − 1 when $ 1000 are deposited into a savings account paying 3 % interest compounded annually and at the end of each year, $ 150 is added to the account. The value of y n is the amount after n years.

Solution Summary: The author explains how the difference equation computes y_n-1 when deposited into a savings account paying 3% interest compounded annually and at the end of each year,

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To calculate: The difference equation computing yn from yn−1 when $1000 are deposited into a savings account paying 3% interest compounded annually and at the end of each year, $150 is added to the account. The value of yn is the amount after n years.

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Chapter 12 Solutions