Question

In: Finance

Sam and Sally are both 30 years old, and beginning in exactly 1 year they will...

Sam and Sally are both 30 years old, and beginning in exactly 1 year they will save $24,000 per year for 30 consecutive years to support their retirement. When they reach retirement at age 60, they will begin to withdrawal an annuity amount per year to enjoy their retirement years. The withdrawals will start in one year, and continue for 25 consecutive years. What is the maximum amount they can withdrawal if interest rates are 3%?

Solutions

Expert Solution

To start with, we will first need to calculate the total amount of money that Sam and Sally can save up until their retirement starting from year 1 of saving till year 30. The key point to keep in mind here is that the interest earned will compounded year on year i.e. the interest earned in Year 1, will itself earn interest in year two. Therefore the easiest way to calculate the saving at the end of 30 years is to construct a table as below. The assumption here is that the saving of $24,000 happens at the end of each year.

The closing balance in each year is the sum of the Opening balance for the year, the investment in the year and the interest earned during the year. The interest in any particular year will be earned on the opening balance for that year, since it is assumed that the saving happens at the end of the year. In excel, this can be achieved by using the formula for future value i.e. FV(3%,30,24000) = $1,141,810

To understand how much is the maximum amount Sam and Sally can withdraw annually, we use the brute force method of calculation. From the above table, at the end of 30 years, Sam and Sally have $1,141,810 as savings. From this amount, a certain amount will be withdrawn at the beginning of each year and the remaining amount will continue to earn interest at 3%. Therefore, closing balance for a particular year will be opening balance minus withdrawals plus interest earned, where interest earned will be 3% of opening balance minus withdrawals.

From the above table, Sam and Sally can withdraw upto $63,661.86 per year for the next 25 years to exhaust their entire corpus in 25 years.

The key assumption in this exercise is that the saving is done at the end of the year and the withdrawal is done at the beginning of the year.


Related Solutions

Sally is a 30-year-old female. She weighs 140 pounds and is 5’6”. Sally is an employee...
Sally is a 30-year-old female. She weighs 140 pounds and is 5’6”. Sally is an employee at a hardware store and walks around the shop periodically throughout the day to help customers. Susan does not have a car, so she walks 0.5 mile to work and from work. After she comes home, she relaxes for the rest of the day. Based on this information about Sally, calculate her estimated energy requirement (EER) and BMI. Age (5 points): 40 years 30...
Sam is 60 years old and recently started relying on cane for last few years. Sam...
Sam is 60 years old and recently started relying on cane for last few years. Sam thinks he may need long-term care services some day in the future. His net worth is around 1 Million and he receives $60,000 per year in a pension. He considers himself to be in excellent health and has never had a serious health situations. Food Sam eats are fairly healthy and includes lots of whole grain and nuts. He also exercises regularly. What is...
1. Sam borrows $1,000,000 by a mortgage with annual payments over 30 years at a rate...
1. Sam borrows $1,000,000 by a mortgage with annual payments over 30 years at a rate of 9.75% per annum interest. What are his annual payments? what is the remaining balance on his loan after 5 years? 15 years? Suppose that 10 years after Sam takes out the loan, the mortgage is sold to an investor who requires a 10.5% rate of return on investments, how much is the investor willing to pay for the loan?
Dean and Brittany are both 32 years old and have a three-year old child, Eddie. They...
Dean and Brittany are both 32 years old and have a three-year old child, Eddie. They came to your office and asked you to build a financial statement analysis for 2017, based on the information provided. Assets: They have $2,350 in their checking account, $12,320 in their money market account, $6,250 in a mutual fund investment account, $4,890 in the 529 plan for Eddie, and $25,000 in their retirement accounts. Their house has a fair market value of $195,320. Dean...
An annuity pays 3 at the beginning of each 3 year period for 30 years. Find...
An annuity pays 3 at the beginning of each 3 year period for 30 years. Find the accumulated value of the annuity just after the final payment, using i (2) = 0.06.
$300,000 loan 6% per year APR 30 year armotization Payable monthly Paid exactly 5 years What...
$300,000 loan 6% per year APR 30 year armotization Payable monthly Paid exactly 5 years What is the loan balance? Please show standard factor notation. Answer should be: $279,163.07
You own 30-year Treasury Bonds that you bought exactly 6 years ago. At the time (you...
You own 30-year Treasury Bonds that you bought exactly 6 years ago. At the time (you bought the TBonds when they were issued), the 30-year T-Bond yield was 3.75% APR (compounded semiannually). That yield was also the coupon rate used to compute the semi-annual coupon payments (the T-Bonds were issued exactly at par). The T-Bonds have a total face value of $50,000. You just received an interest payment, and the bonds will mature in exactly 24 years. You check today’s...
a.Your brother is saving for his daughter (3‐year‐old Monica) to start college in exactly 15 years...
a.Your brother is saving for his daughter (3‐year‐old Monica) to start college in exactly 15 years (t=15) from today (t=0). A single year of college today (t=0) would cost him $25,000. If college costs increase at an annual rate of 3.5%, what will each year of college cost for the four years his daughter is in college (t=15 – age 18, t=16 – age 19, t=17 – age 20, and t=18 – age 21)? b. University offers your brother the...
Moses agrees to buy a car from Sally, thinking that it is only 2 years old...
Moses agrees to buy a car from Sally, thinking that it is only 2 years old with less than 10,000 km driven in it. In fact the car is 5 years old car and has been driven over 120,000 km. As the purchase price is to be paid over 3 years, Sally requires that Moses have George provide a guarantee. Some months later, Moses learns the truth about the car and stops making his monthly payments to Sally. Sally makes...
In 2019, Sam is single, 35 years old, rents an apartment for 400 a month and...
In 2019, Sam is single, 35 years old, rents an apartment for 400 a month and makes a charitable contribution of 3,000. Sam’s AGI is 47,000. Sam’s taxable income is: (a) 32,000 (b) 34,800 (c) 44,000 (d) 42,000 Taxable income for an individual can be: (a) AGI reduced by itemized deductions (b) AGI reduced by personal and dependency exemptions (c) AGI reduced by the greater of standard deduction or itemized deductions (d) AGI reduced by deductions from AGI and personal...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT