Question

________1. Randy Hill wants to retire in 10 years with $500,000. He can earn 6% per year on his investments. Compute how much he needs to deposit each year to reach his goal. ________2. Joe Morris wants to start a savings fund from which his grandson could withdraw $3,000 a year for 10 years. The fund would earn 5% interest. Compute the amount Joe would have to deposit now to reach his goal. ________3. Your rich aunt has offered to finance five years of college for you. The annual cost will be $30,000 and the interest rate is 5%. Compute how much money your aunt must give you now to finance the five years of college. ________4. Assume your father is 55 and wants to retire at age 65 with $300,000 in a retirement fund. The interest rate is 8%. Compute how much he must deposit at age 55 to accumulate the $300,000. ________ 5. Assume you want to have $25,000 for a down payment for a house in five years. Compute the amount you would need to deposit today. Your money will earn 5 percent. ________ 6. Jeff Renfro is planning to go to graduate school (Ph.D) in a program of study that will take six years. Jeff wants to have $35,000 available each year for various school and living expenses. He can earn 5 percent on his money. Compute how much he must deposit at the start of his studies to be able to withdraw $35,000 a year for six years. ________7. Angie Baden deposits $10,000 a year into her retirement account. These funds will earn 8 percent over the 10 years until her retirement. Compute what the value of her retirement account will be when she retires. ________8. Assume you borrow $80,000 with a 7 percent interest rate, to be repaid in seven equal yearly payments. Compute the amount of each payment.

Answer 1

Solution:

There are 8 separate questions having no link with each other. So I am giving the answer of 1^st question. For remaining, please ask separate question for each part…

1. Randy Hill wants to retire in 10 years with $500,000. He can earn 6% per year on his investments. Compute how much he needs to deposit each year to reach his goal.

Solution:

Randy needs to deposit an amount each year to get $500,000 in 10 years.

Here, the question is related to the ordinary annuity. Under ordinary annuity, the payment or receipts or savings are occurred at the end of the year for a specified period of time.

Future Value of Ordinary Annuity = $500,000

Number of period = 10

Interest Rate (R) = 6% per year

Future Value factor of Ordinary Annuity for 10 periods at 6% = ((1+R)ⁿ – 1) / R

= (1+0.06)¹⁰ - 1) / 0.06

= 13.18079

Note – decimal places are rounded to 5 decimal places

Future Value of Ordinary Annuity = Yearly Saving Amount x Future value Ordinary annuity interest factor for 10 periods at 6%

$500,000 = Yearly Saving Amount x 13.18079

Yearly Saving Amount = $500,000 / 13.18079 = $37,934

Randy needs to deposit each year $37,934 to reach his goal.

In case the factor is rounded to 3 decimal places, the answer will be different.

Hope the above calculations, working and explanations are clear to you and help you in understanding the concept of question.... please rate my answer...in case any doubt, post a comment and I will try to resolve the doubt ASAP…thank you