Problem 4: You are working for a finance firm and a client comes to you and want
ID: 2765083 • Letter: P
Question
Problem 4: You are working for a finance firm and a client comes to you and wants to know how much money they should put in an annuity (which earns 2.412% interest compounded quarterly) at the end of each three months for the next 46 years. Their goal is that when they retire at the end of46 years, they would like the quarterly withdrawals from the annuity to total $63,000 per year and that the annuity is to last for the next 26 years. You are to determine the amount which your client needs to deposit into the annuity at the end of each three months for the next 46 yearsso that they can meet their retirement goal. Do the following:
A. Show all your work that you used to answer this problem. Label the steps and important values as you solve the problem. Note that when you use the TVM Solver, show the all variables and the values you entered (into the variables) and solved for. (10 points)
B. Find the total amount of interest the client will earn (from the time they start contributing to the account to when they make the last withdrawal). Show how you arrived at the answer. (2 points)
Problem 4 You are working for a finance firm and a client comes to you and wants to know how much money they should put in an annuity (which earns 2.412% interest compounded quarterly) at the end of each three months for the next 46 years. Their goal is that when they retire at the end of 46 years, they would like the quarterly withdrawals from the annuity to total $63,000 per year and that the annuity is to last for the next 26 years. You are to determine the amount which your client needs to deposit into the annuity at the end of each three months for the next 46 years so that they can meet their retirement goal. Do the following: A. Show ail your work that you used to answer this problem. Label the steps and important values as you solve the problem. Note that when you use the TVM Solver, show the all variables and the values you entered (into the variables) and solved for. (10 points) Find the total amount of interest the client will earn (from the time they start contributing to the account to when they make the last withdrawal). Show how you arrived at the answer. (2 points) B.Explanation / Answer
A)
The annual withdrawal of Annuity as retirements pay-outs= 63000
The quarterly withdrawal of Annuity as retirements pay-outs=63000/4 =15750 (since there are 4 quarter in a year)
The a/c earns 2.412% per quarter during the retirement period of 26 years or 4*26=104 quarters.
Therefore the present value of Retirement withdrawals @ 2.412% per quarter withdrawing 15750 per quarter for 104 quarters (at time of retirement)
=(15750/.02412)*(1-1/(1.02412)^104)
=652985.07462687*(1-0.0838516968533)
=$ 598231.1681
This present value (PV) of retirement withdrawals at time of retirement should be the future value of all the savings done during the 46 years before retirement. Therefore the balance at retirement should be the present value (PV) of retirement withdrawals.
Thus the Balance at retirement required=$ 598231.1681
Before retirement the savings should be done during the 46 years or 46*4=184 quarters into an a/c earning 2.412% per quarter
Future value of all the annual savings at time of retirement
=(annual saving/.02412)*((1.02412)^184-1)
Which must equal present value (PV) of retirement withdrawals at time of retirement so that all the withdrawals during the retirement met.
Therefore,
$ 598231.1681=(annual saving/.02412)*((1.02412)^184-1)
=> annual saving=(598231.1681*.02412)/((1.02412)^184-1)
=14429.335774572/(80.27049624-1)
=$182.03
Therefore $182.03 should put in an annuity (which earns 2.412% interest compounded quarterly) at the end of each three months for the next 46 years to meet the retirement goal.
B)
Total sum of contributions made by client=Total savings done=$184*182.03=$33493.52
Total sum of withdrawals made by client=$104*15750=$1638000
Total amount of interest earned=total sum of withdrawals made by client- total sum of contributions made by client
Total amount of interest earned= $1638000-$33493.52
Total amount of interest earned =$1604506.48