question archive This is a classic retirement problem
This is a classic retirement problem
Subject:AccountingPrice:3.86 Bought15
This is a classic retirement problem. Your friend, Mary Jones, is celebrating her 30th birthday and wants to start saving for her anticipated retirement. She has the following years to retirement and retirement spending goals, which are as follows:
Years until retirement: 30
Amount to withdraw each year upon retirement: $90,000
Years to withdraw in retirement: 20
Interest rate: 5%
Mary is planning to make equal annual deposits into her retirement account, while her first withdrawal will take place one year after her last deposit.
For purposes of answering the following questions, feel free to use Excel or your calculator---but you must show your work and how you arrived at your answers.
Please answer the following five questions.
HINT: To answer these questions, first, you need to know how much Mary will need when she is ready to retire. Since this amount will be the same for each of the first four questions below.
1. If Mary starts making these deposits in one year and makes her last deposit on the day she retires, what amount must she deposit annually to be able to make the desired withdrawals at retirement?
2. What if Mary starts making these deposits when she turns 40 years old and only has 20 years left to retirement, what amount must she deposit annually to be able to make the same desired withdrawals?
3. Suppose Mary (on her 30th birthday) has just inherited a large sum of money. Rather than making equal annual payments, she has decided to make one lump sum deposit today to cover the entire cost of her retirement, how much would she need to deposit today to cover the anticipated withdrawals?
4. Assume the same scenario as No. 3 above, but the interest rate she can earn over the next 30 years is only 3%; what would she need to deposit today to cover the anticipated withdrawals?
5. When you compare the results of No. 1 and No. 2 above, what is the key factor that causes the results to be so different?
Purchase A New Answer
Custom new solution created by our subject matter experts
GET A QUOTE
Answer Preview
First, we will calculate the Present Value of Retirement Fund.
Formula
PV = PMT / r * [1 - 1/(1 + r)^n]
Where,
n = Years to withdraw in retirement
r = Interest rate
PMT = Amount to withdraw each year upon retirement
PV = 90000 / 0.05 * [1 - 1/ (1 + 0.05)^20]
PV = 1800000 * [1 - 0.376889]
PV = 1800000 * 0.623111
PV = 1121600
1) From above calculation fund required after 30 years is 1121600
Now we will calculate deposit required each month
FV = PMT / r * [(1 + r)^n -1]
1121600 = PMT / 0.05 * [(1 + 0.05)^30 - 1]
1121600 * 0.05 = PMT * 3.321942
56080 = PMT * 3.321942
PMT = 16881.69
she must deposit $ 16881.69 annually to be able to make the desired withdrawals at retirement
2) If she start deposit at age 40
FV = PMT / r * [(1 + r)^n -1]
1121600 = PMT / 0.05 * [(1 + 0.05)^20 - 1]
1121600 * 0.05 = PMT * 1.653298
56080 = PMT * 1.653298
PMT = 33920.09
she must deposit $ 33920.09 annually to be able to make the desired withdrawals at retirement
3) Let the amount to be deposited be Y
Y (1 + 0.05)^30 = 1121600
Y * 4.321942 = 1121600
Y = 259513
she need to deposit $ 259513 today to cover the anticipated withdrawals
4) Interest rate 3%
Y (1 + 0.03)^30 = 1121600
Y * 2.427262 = 1121600
Y = 462084
she need to deposit $ 462084 today to cover the anticipated withdrawals
5)
When we compare results of No. 1 and No. 2 above, annual deposit increased by $ 17038.40 ( 33920.09 - 16881.69)
In the above calculation interest rate was same, the only factor affected the calculation was time left for retirement. In the first calculation time of retirement was 30 years and in second calculation, it was only 20 years which have affected the increase in annual deposit to achieve the required goal.
