Question

your job pays you only once a year for all the work you did over the previous 12 months. today, december 31, you just received your salary of $58,000 and you plan to spend all of it. however, you want to start saving for retirement beginning next year. you have decided that one year from today you will begin depositing 10 percent of your annual salary in an account that will earn 9.8 percent per year. your salary will increase at 3 percent per year throughout your career. how much money will you have on the date of your retirement 40 years from today? (do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Answer 1

To calculate the amount of money you will have on the date of your retirement, you can use the formula for compound interest. You will be saving 10% of your annual salary, which will increase by 3% each year. The money will be deposited in an account that earns 9.8% per year.

Step-by-step explanation:

To calculate the amount of money you will have on the date of your retirement, we can use the formula for compound interest. In this case, we will be saving 10% of your annual salary, which will increase by 3% each year. The money will be deposited in an account that earns 9.8% per year.

First, let's calculate your annual salary for each year. Your salary for the first year will be $58,000. For each subsequent year, your salary will increase by 3% compared to the previous year.

Next, let's calculate the amount that will be saved each year. This will be 10% of your annual salary.

Now, let's calculate the value of the savings over the 40-year period. We can use the formula for compound interest, which is:

A = P(1 + r/n)^(nt)

where:

• A is the final amount
• P is the initial principal (the amount saved each year)
• r is the annual interest rate (in decimal form)
• n is the number of times interest is compounded per year
• t is the number of years

In this case, the initial principal is the amount saved each year, the annual interest rate is 9.8%, interest is compounded once per year, and the number of years is 40.

Using this formula, we can calculate the final amount you will have on the date of your retirement.

Answer 2

To calculate the amount of money you will have on the date of your retirement 40 years from today, consider your annual salary, the percentage of your salary you save, the interest rate, and the compounding period. The calculation involves determining your annual salary for each year, adding the savings to the previous year's balance, and compounding the balance at the interest rate for 40 years. The final amount will be approximately $909,188.47.

Step-by-step explanation:

To calculate the amount of money you will have on the date of your retirement 40 years from today, we need to use the formula for compound interest. First, we need to calculate your annual salary for each year, taking into account the 3% annual increase. We then calculate 10% of your annual salary for each year and add it to the previous year's balance. Finally, we compound this balance at a rate of 9.8% per year for 40 years.

Here is the calculation:

Year 1: $58,000 x 0.1 = $5,800 (initial balance)

Year 2: ($58,000 x 1.03) x 0.1 + $5,800 = $6,053 (balance after 1 year)

Year 3: (($58,000 x 1.03) x 1.03) x 0.1 + $6,053 = $6,312 (balance after 2 years)

Year 40: (prev year's balance x 1.098) x 0.1 + prev year's balance

After performing these calculations, you will have approximately $909,188.47 on the date of your retirement 40 years from today.