Question

I need help answering this question and understanding the formulas that need to be used to properly answer this question.

Thank you

Emily Dorsey's current salary is $90,000 per year, and she is planning to retire 23 years from now. She anticipates that her annual salary will increase by $4.000 each year $90,000 the first year, to $94,000 the second year, $98,000 the third year and s forth and she plans to deposit 5% of heryea sala int a retirement un hat % 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

Here it is given the 9% interest rate will be compounded daily. Now we will find the effective interest rate.

i= (1 + r/N)^N - 1

Here, r = 9%

N = 365

i= (1 +0.09/365)^365 - 1 = 9.42%

Now there will be increase of $4000 in salary. So below will be series of salaries-

90000, 94000, 98000, 102000...........

5% of the salary will be deposited into retirement funds. So, amount of deposits will be-

4500, 4700, 4900, 2100.....

So there is change of 200 between two deposits.

Using the geometric series method, we can calculate the accumulated value of deposits

FV = 4500 ( F/A,9.42%,23) + 200 (P/G,9.42%,23)(F/P,9.42%,23)

By use of engineering economic calculator -

FV = 4500 * 71.8016 + 200 * 69.1805 * 7.6344

FV = 428737.522 ~ $428738