Could you please show your work, step by step if possible? Thank you! Problem 1.

Question

Could you please show your work, step by step if possible? Thank you!

Problem 1. (10 pts) Elon Musk is an entrepreneur, is 47 years old, and his salary next year will be $45,760 (California minimum wage). Mr. Musk expects that California's minimum wage will increase at a steady rate of 5% per year until his retirement age at 65, If he saves the 20% of his salary each year and invests these savings into a Low Fee Mutual Index Fund at an interest rate of 8%, how much will he have at his retirement (based only on his salary)? (Based on problem 2.57) Sources https://www.investopedia.com/news/elon-musk-earns-californias-minimum-wage-ceos-tsla/ https://www.moneyunder30.com/percentage-of-income-should-you-save-every-month

Explanation / Answer

Salary on the 48th year = $45,760

It will increase by 5% every year up to the retirement age of 65 years

Hence, number of years in this question will be 18 years

20% of the salary (0.20*$45,760 = 9,152) he will deposit in Mutual index fund at an interest rate of 8%.

Calculate the amount he can save at the end of 65 (retirement age) year.

Since there is no formula to calculate the future worth of geometric gradient series, we have to calculate the present worth first and then can calculate the future worth.

Present Value = A1 [1 – (1+g) N (1+i) –N ÷ i – g]

Present Value = $9,152 [1 – (1+.05) 18 (1+.08) –18 ÷ .08 – .05]

Present Value = $9,152 [0.3977 ÷ 0.03]

Present Value = $9,152 [13.2567] = $121,325

Future Value of $121,325

Future Value = P (F/P, 8%, 18)

Future Value = $121,325 (3.9960) = $484,815

The amount he can save at the end of 65 (retirement age) year will be $484,815.

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