Final answer:
The present worth of an engineer's retirement fund after 35 years with an initial salary of $80,000, 5% annual increment, and 15% annual deposit at 5% interest can be calculated using geometric series for the salary increase and present value formulas for the deposits.
Step-by-step explanation:
The subject of this question is Mathematics, specifically focusing on financial mathematics in the context of retirement savings and present worth valuation. To determine the present worth of a retirement fund after 35 years, given an annual salary increment and a constant deposit percentage, we use the formulas for geometric series to account for the salary increase and the formula for present value to discount future values to today's dollars.
An engineer deposits 15% of her annual salary, which currently stands at $80,000, into a retirement fund. Her salary is expected to increase by 5% annually. Over 35 years, deposits will grow at a rate that combines both the salary increment and the 5% interest rate on the retirement fund.
The calculation involves summing the present values of all future deposits. For each year, the deposit is 15% of the salary, which itself is increasing by 5% each year. Then, each deposit's future value is discounted back to the present using the formula PV = FV / (1 + r)^n, where PV is the present value, FV is the future value, r is the interest rate, and n is the number of years until the deposit is made.
To calculate the total present worth, we sum the present values of all the engineer's deposits over the 35-year period. This needs a financial calculator or software that can handle such complex calculations.