. Assume you will need $30,000 each year over the next 20 years to live at the s
ID: 2664867 • Letter: #
Question
. Assume you will need $30,000 each year over the next 20 years to live at the standard you desire. Also estimate the rate of return you can reasonably expect to earn annually, on average, during that 20 year period by investing in a stock portfolio similar to the S&P 500 (e.g. 9%).a. How large a single lump sum would you need today to provide the annual cash required to allow you to live at the desired standard over the next 20 years?
b. Would the lump sum calculated in part a. be larger or smaller if you would have invested in a bond portfolio (e.g. 6%)? Explain.
c. What conclusions do you draw for your retirement investments?
Explanation / Answer
According to the given problem, Annual payment amount = $30,000 Number of years = 20 Interest rate = 9% Now, we have to calculate the present value of annuity. a) Calculating the present value of annuity using excel sheet: Step1: Go to excel and click "insert" to insert the function Step2: Select the "PV" function as we are finding the present value of annuity in this case. Step3: Enter the values as Rate = 9%; Nper = 20; PMT = -30000; FV = 0 Step4: Click "OK" to get the desired value. The value comes to "$273,856.37" Therefore, the present value of annuity is $273,856. b) Calculating the present value of annuity for the second alternative. Step1: Go to excel and click "insert" to insert the function Step2: Select the "PV" function as we are finding the present value of annuity in this case. Step3: Enter the values as Rate = 6%; Nper = 20; PMT = -30000; FV = 0 Step4: Click "OK" to get the desired value. The value comes to "$344,097" Therefore, the present value of annuity at 6% is $344,097 The present value of ordinary annuity is the value of a stream of expected or promised future payments that have been discounted to a single equivalent value today. It is extremely useful for compating two seperate cash flows that differ in some way. It can be thought of the amount that must be invested today at a specific interest rate so that when you withdraw an equal amount each period, the original principal and all accumulated interest will be completely exhausted at the end of annuity. The present value of annuity at 9% is less than present value of annutiy at 6%. c) The investment decision should be to choose the present value of annuity at 9% as todays investment will be less when compared to the present value at 6% where we need to invest a large amount today. So Present value of annuity at 9% interest rate should be choosen. Step1: Go to excel and click "insert" to insert the function Step2: Select the "PV" function as we are finding the present value of annuity in this case. Step3: Enter the values as Rate = 6%; Nper = 20; PMT = -30000; FV = 0 Step4: Click "OK" to get the desired value. The value comes to "$344,097" Therefore, the present value of annuity at 6% is $344,097 The present value of ordinary annuity is the value of a stream of expected or promised future payments that have been discounted to a single equivalent value today. It is extremely useful for compating two seperate cash flows that differ in some way. It can be thought of the amount that must be invested today at a specific interest rate so that when you withdraw an equal amount each period, the original principal and all accumulated interest will be completely exhausted at the end of annuity. The present value of annuity at 9% is less than present value of annutiy at 6%. c) The investment decision should be to choose the present value of annuity at 9% as todays investment will be less when compared to the present value at 6% where we need to invest a large amount today. So Present value of annuity at 9% interest rate should be choosen.Related Questions
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