An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?
Answer (1)
Calculate the annual income: 7415 × 12 = 88980 .
Determine the annual consumption to maintain a stable life: 45 2703921 = 60087.13 .
Calculate the annual savings needed to maintain stable consumption in retirement: S = 30 866785.95 = 28892.87 .
The worker needs to save SZL28,892.87 each year during their working years to maintain stable consumption in retirement. 28892.87
Explanation
Calculate Annual Income First, we need to calculate the worker's annual income. The worker's monthly income is SZL7,415.00, so the annual income is: 7415 × 12 = 88980
Calculate Working and Retirement Years Next, we calculate the number of working years and retirement years. Working years: 70 − 40 = 30 years. Retirement years: 85 − 70 = 15 years.
Calculate Annual Consumption i. To maintain a stable life, the worker needs to distribute their total resources (accumulated wealth + total lifetime income) over their remaining life expectancy. The total lifetime income is: 88980 × 30 = 2669400 The total resources available are: 2669400 + 34521 = 2703921 The remaining life expectancy is: 85 − 40 = 45 Therefore, the annual consumption should be: 45 2703921 = 60087.13
Calculate New Annual Consumption ii. If the worker wins a SZL150,000 lottery, the new total resources are: 2703921 + 150000 = 2853921 The new annual consumption would be: 45 2853921 = 63420.47
Calculate Marginal Propensity to Consume iii. The marginal propensity to consume (MPC) is the change in consumption divided by the change in income (lottery winnings): MPC = 150000 63420.47 − 60087.13 = 150000 3333.34 = 0.0222
Calculate Total Lifetime Consumption iv. The total lifetime consumption is equal to the total resources available, which we calculated in part i: 2703921
Calculate Portion of Lifetime Consumption from Current Wealth v. The portion of the worker's total lifetime consumption that comes from current wealth is: 2703921 34521 = 0.0128
Calculate Total Income Until Retirement vi. The total income the worker will earn from now until retirement is: 88980 × 30 = 2669400
Calculate Annual Savings Needed for Retirement vii. Let S be the annual savings. The accumulated savings at retirement will be the initial wealth plus the accumulated savings: Wealth + S * Number of working years. The consumption during retirement years will be equal to the resources at retirement divided by the number of retirement years. Set up an equation to solve for S such that the consumption during retirement is equal to the stable consumption calculated in step i. ( W e a lt h + S × w or kin g _ ye a rs ) / re t i re m e n t _ ye a rs = ann u a l _ co n s u m pt i o n ( 34521 + S × 30 ) /15 = 60087.13 34521 + 30 S = 60087.13 × 15 30 S = 901306.95 − 34521 30 S = 866785.95 S = 30 866785.95 = 28892.87 The worker needs to save SZL28,892.87 each year during their working years to maintain stable consumption in retirement.
Examples
Understanding lifetime consumption and savings is crucial for financial planning. For instance, knowing how much to save each year to maintain a desired lifestyle during retirement helps individuals make informed decisions about their spending and investment strategies. This type of calculation is also essential for governments and financial institutions when designing social security systems and retirement plans, ensuring people can maintain financial stability throughout their lives. By planning effectively, individuals can secure their financial future and enjoy a comfortable retirement.
