30.03.2023 - 04:10

A 20-year-old student wants to save $5 a day for her retirement. Every day, she places $5 in a drawer. At the end of EACH year, she invests the accumulated savings in an automated account with an expected annual return of 9%, paid annually. A) If she beg

Question:

A 20-year-old student wants to save $5 a day for her retirement. Every day, she places $5 in a drawer. At the end of EACH year, she invests the accumulated savings in an automated account with an expected annual return of 9%, paid annually.

A) If she begins saving today; How much money will she have when she is 65?

B) If she did not start saving until she was 45 years old, how much would she have at 65?

C) How much must the 45-year-old deposit monthly to catch the 20-year old?

Answers (1)
  • frz-
    April 5, 2023 в 21:46

    A) If the student begins saving today, she has 45 years left until she reaches the age of 65. She saves $5 a day, which is $1,825 per year ($5 x 365 days). At the end of each year, she invests the accumulated savings with an expected annual return of 9%. Therefore, the future value of her savings can be calculated using the formula for the future value of an annuity:

    FV = PMT x [(1 + r)^n - 1]/r

    Where FV is the future value, PMT is the payment (in this case, $1,825), r is the interest rate per period (in this case, 9%/year), and n is the number of periods (in this case, 45 years).

    Substituting the values, we get:

    FV = $1,825 x [(1 + 0.09)^45 - 1]/0.09 FV = $1,825 x [132.64]/0.09 FV = $1,825 x 1,473.77 FV = $2,691,540.25

    Therefore, if the student begins saving today, she will have $2,691,540.25 when she reaches the age of 65.

    B) If the student starts saving when she is 45 years old, she has only 20 years left until she reaches the age of 65. She saves $5 a day, which is $1,825 per year ($5 x 365 days). At the end of each year, she invests the accumulated savings with an expected annual return of 9%. Therefore, the future value of her savings can be calculated using the same formula as above, with n = 20.

    FV = $1,825 x [(1 + 0.09)^20 - 1]/0.09 FV = $1,825 x [5.604]/0.09 FV = $1,825 x 62.27 FV = $113,515.75

    Therefore, if the student starts saving when she is 45 years old, she will have $113,515.75 when she reaches the age of 65.

    C) To catch up with the 20-year-old, the 45-year-old needs to accumulate the same amount of savings by the time she reaches 65. She has only 20 years left to save, so she needs to save more each year than the 20-year-old. Let's call the monthly deposit that the 45-year-old needs to make x. Then, the future value of her savings can be calculated using the same formula as above, with PMT = 12x and n = 20.

    FV = 12x x [(1 + 0.09)^20 - 1]/0.09 FV = 12x x [5.604]/0.09 FV = 12x x 62.27 FV = 747.24x

    We want the future value of the 45-year-old's savings to be equal to the future value of the 20-year-old's savings, which is $2,691,540.25. Therefore,

    747.24x = $2,691,540.25 x = $3,603.73

    Therefore, the 45-year-old needs to deposit $3,603.73 per month to catch the 20-year-old.

Do you know the answer?
Not sure about the answer?
Find the right answer to the question A 20-year-old student wants to save $5 a day for her retirement. Every day, she places $5 in a drawer. At the end of EACH year, she invests the accumulated savings in an automated account with an expected annual return of 9%, paid annually. A) If she beg by subject Accounting, and if there is no answer or no one has given the right answer, then use the search and try to find the answer among similar questions.
Search for other answers
New questions in the category: Accounting
Authorization
*
*

Password generation