Question

Emily Dorsey's current salary is $73,000 per year, and she is planning to retire 15 years from now. She anticipates that her annual salary will increase by $3,000 each year ($73,000 the first year, to $76,000 the second year, $79,000 the third year, and so forth), and she plans to deposit 5% of her yearly salary into a retirement fund that earns 9% interest compounded daily. What will be the amount of interest accumulated at the time of Emily's retirement? Assume 365 days per year. The amount of interest accumulated at the time of Emily's retirement will be $ thousand. (Round to the nearest whole number.)

Answer 1

Step-by-step explanation: To calculate the amount of interest accumulated at the time of Emily's retirement, we can use the formula for compound interest:

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=

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×

(

1

+

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)

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A=P×(1+

n

r

​

)

nt

Where:

A is the final amount including both the principal and the interest.

P is the initial principal (the amount deposited each year into the retirement fund).

r is the annual interest rate (as a decimal).

n is the number of times the interest is compounded per year.

t is the number of years.

In this case, Emily plans to deposit 5% of her yearly salary into the retirement fund, which will increase each year, and the interest is compounded daily (365 times a year).

Let's break down the steps to calculate the interest accumulated:

Calculate the annual deposit for each year based on Emily's increasing salary.

Calculate the interest accumulated for each year's deposit.

Sum up the interest accumulated for all the years.

Here's the calculation:

Annual Deposit Calculation:

Year 1: 5% of $73,000 = $73,000 * 0.05 = $3,650

Year 2: 5% of $76,000 = $76,000 * 0.05 = $3,800

Year 3: 5% of $79,000 = $79,000 * 0.05 = $3,950

...

Interest Accumulation Calculation:

For each year's deposit, calculate the amount of interest accumulated at the end of 15 years using the compound interest formula with

P as the deposit for that year,

r as 0.09 (9% interest),

n as 365 (daily compounding), and

t as 15 years.

Sum up the interest accumulated for all the years to get the total amount of interest.

After performing these calculations, you should be able to determine the amount of interest accumulated at the time of Emily's retirement. Remember to round the final answer to the nearest whole number, as specified.