Question

In: Finance

Your uncle has $300,000 today. Assume he can earn 9.18% on his investments. He now wants...

Your uncle has $300,000 today. Assume he can earn 9.18% on his investments. He now wants to retire in 10 years. Here is his situation:

a. He wants to withdraw $35,000 every two years, beginning 12 years from today for 10 equal, every two-year (i.e. every other year) withdrawals.

b. He has to pay for his daughter’s college beginning in 5 years at $20,000 for four years (i.e. he has to make a payment in year 5, 6, 7, and 8).

c. He just inherited some money, totaling $40,000, which he will receive 8 years from today.

He also wants to leave you whatever he can afford 20 years from today and still meet all his other goals. How much is the amount of money you will receive?

Solutions

Expert Solution

Value of today's investments = $300,000

Annual interest rate = 9.18%

2 year interest rate = (1+Annual interest rate)² -1 = (1+9.18%)² -1 = 19.2027%

Years to retirement = 10 years

He needs to withdraw $35,000 every 2 years for 10 equal withdrawals

The retirement amount he needs at retirement can be calculated using the PV for an ordinary annuity formula

Where C is the withdrawal = $35,000

i = 2 year interest rate = 19.2027%

n = number of 2 year periods = 10

PV = $150,799.67

Your uncle needs $150,799.67 at retirement

Retirement fund = $150,799.67

He has to pay for his daughter’s college beginning in 5 years at $20,000 for four years

Present value of these payments at year 5 can be calculated using the PV for an annuity-due formula

Where C is yearly payment = $20,000

i = annual interest rate = 9.18%

n = number of periods = 4

PV = $70,463.93

Your uncle needs $70,463.93 at the end of 5 years for his daughter's college

Value of his initial investments after 5 years = Value of today's investments *(1+9.18%)⁵

= $300,000 *(1+9.18%)⁵ = $465,411.07

Value of the above investment after accounting for daughter's college = Value of his initial investments after 5 years - Present value of amount needed for daughter's college

= $465,411.07 - $70,463.93 = $394,947.14

Value of the investments in 2 after another 3 years (at year 8) = $394,947.14 *(1+9.18%)³ = $514,006.06

Value of the above investment after accounting for inheritance = Value of investments at year 8 + inheritance

= $514,006.06 + $40,000 = $554,006.06

Value of the investments in 5 after 2 years at his retirement (at year 10) = $554,006.06 *(1+9.18%)² = $660,390.32

Value of the above investment after accounting for retirement = Value of investments at retirement - retirement fund

= $660,390.32 - $150,799.67 = $509,590.65

Value of the above investment after another 10 years (at year 20) = $509,590.65*(1+9.18%)¹⁰ = $1,226,457.06

This is the amount that you will receive

You will receive $1,226,457.06 after 20 years

jeff jeffy answered 1 year ago

Next > < Previous

Related Solutions

1) Your uncle has $300,000 invested at 7.5%, per annum and he now wants to retire....

1) Your uncle has $300,000 invested at 7.5%, per annum and he now wants to retire. He wants to withdraw $35,000 at the beginning of each year, starting immediately. He also wants to have $25,000 left to give Katya when he ceases to withdraw funds from the account. For how many years can he make the $35,000 withdrawals and still have $25,000 left in the end? a. 15 b. 13.5 c. 13.5 d.11.9 2. Which statements is TRUE? a, firms...

Your uncle has $320,000 invested at 7.5%, and he now wants to retire. He wants...

Your uncle has $320,000 invested at 7.5%, and he now wants to retire. He wants to withdraw $35,000 at the end of each year, starting at the end of this year. He also wants to have $25,000 left to give you when he ceases to withdraw funds from the account. For how many years can he make the $35,000 withdrawals and still have $25,000 left in the end? a. 12 years b. 16 years c. 15 years d. 17...

Your uncle has 431,000 invested at 6.8% and he now wants to retire. He plans to...

Your uncle has 431,000 invested at 6.8% and he now wants to retire. He plans to withdraw $40,000 at the end of each year, beginning this year. How many years will it take to exhaust his funds, i.e., run the account down to zero?

Your uncle Abdallah is celebrating his 33th birthday today and wants to start saving for his...

Your uncle Abdallah is celebrating his 33th birthday today and wants to start saving for his retirement at the age of 63. He wants to be able to withdraw AED 100,000 from his saving account on each birthday for 20 years following his retirement. The first withdraw will be on his 64th birthday. Your uncle intends to invest his money in a local bank in Abu Dhabi that offers 7% interest rate per year. He wants to make equal payments...

1. Your uncle is planning for retirement, and he wants to buy an annuity that will...

1. Your uncle is planning for retirement, and he wants to buy an annuity that will provide him with $96,000 of income a year for 20 years, with the first payment coming immediately. The market rate on this annuity is 5.25%. How much would the cost be today? Answer just the dollar amount without the + or - sign. Round to the nearest dollar. 2. What's the value today of $1,950 to be received in 5 years if the appropriate...

Assume you can earn 8.3% per year on your investments. a. If you invest $190,000 for...

Assume you can earn 8.3% per year on your investments. a. If you invest $190,000 for retirement at age 30, how much will you have 35 years later for retirement? b. If you wait until age 40 to invest the $190,000, how much will you have 25 years later for retirement? c. Why is the difference so large? (Round to the nearest dollar.)

Your uncle has recently retired with two million dollars of superannuation funds. He wants to invest...

Your uncle has recently retired with two million dollars of superannuation funds. He wants to invest a part of his super fund to fixed income securities, preferably foreign government bonds. He found Germany Government bonds offering YTM of 3% whereas Greece Government bonds offering YTM of 5%. He got confused with two different rates since both of them are risk-free government bonds. Explain your uncle the underlying cause of 2% differences in YTM between these two Government bonds. Assume your...

Your uncle has recently retired with two million dollars of superannuation funds. He wants to invest...

4. Now assume that your wealthy grandfather wants to invest some money in your behalf. He...

4. Now assume that your wealthy grandfather wants to invest some money in your behalf. He wants the money to be worth $65,000 on December 31, 2025. How much money will he need to invest on a one-time basis on December 31, 2020 in order to earn enough interest to accumulate to $65,000 by December 31, 2025? Assume a 5% interest rate. (Hint: I recommend that you use the PV formula in Excel to solve this problem.) Use the information...

Assume you can earn 9% per year on your investments. If you invest $100,000 for retirement...

Assume you can earn 9% per year on your investments. If you invest $100,000 for retirement at age 30, how much will you have 35 years later for retirement? (Answer: $2,041,397) If you wait until age 40 to invest the $100,000, how much will you have 25 years later for retirement? (Answer: $862,308) Why is the difference so large?

Subjects