The monthly income from section two above is in today’s dollars. If prices of th
ID: 2788926 • Letter: T
Question
The monthly income from section two above is in today’s dollars. If prices of these items increase each year from now until you retire, you will need substantially more income at retirement just to maintain the same standard of living. This is the effect of inflation. The problem one runs into is estimating, with any degree of accuracy, what inflation will be in the future. The actual consumer price index figures for several years are listed below. To get an idea of the actual rate of inflation each year over each of these 5 year periods, compute the average annual compound rate of growth in prices (the average annual inflation rate) over each of the five year periods using time value of money concepts. (hint: the rate of inflation is the compound growth in prices, just like the compound growth of money, this is like solving for the interest rate (I/Y if you know the PV and FV over each 5 year time period.)
Date CPI* Average Annual Growth Rate in CPI
1970 38.8 (Please show your Calculator inputs!)
______%_
1975 53.8
______%_
1980 82.4
______%_
1985 107.6
______%_
1990 130.7
______%_
1995 152.4
_______%
2000 175.3
_______%
2005 195.3
_______%
2010 218.1
As you can see, there have been many years in the not too distant past in which inflation has been significant. The average rate of inflation over the last 75 years has been approximately 3% per year. Assume that inflation will average this amount over the coming years, calculate the future value of the Annual pretax income needed that you calculated at the bottom of page one in number 2. (See *), if it is growing by the rate of inflation each year from now until you retire. $__________________** (calculate on an annual basis) N is not 1!
Explanation / Answer
To solve this use either compounded interest table or linear interpolation or Pv function in excel We are using linear interpolation here - r 5 year compounded amount of $1 5% 1.276282 r 1.386598 8% 1.469328 8-r/8-5 = 1.4693-1.3866/1.4693 - 1.2763 8-r = 0.08273/0.193047 x 3 r=8 - 1.28565 r= 6.71435 (approx) * 1975 - 80 = 53.8 x (1+r)^5 = 82.4 (1+r)^5 = 82.4/53.8 (1+r)^5 = 1.590734 To solve this use either compounded interest table or linear interpolation or Pv function in excel We are using linear interpolation here - r 5 year compounded amount of $1 5% 1.276282 r 1.531599 10% 1.61051 10-r/10-5 = 1.6105 - 1.5316/1.6105 - 1.2763 10-r = 0.07891/0.3342 x 5 r=10 - 1.1805 r= 8.8195 * 1980 - 85 = 82.4 x (1+r)^5 = 107.6 (1+r)^5 = 107.6/82.4 (1+r)^5 = 1.305825 To solve this use either compounded interest table or linear interpolation or Pv function in excel We are using linear interpolation here - r 5 year compounded amount of $1 5% 1.276282 r 1.305825 10% 1.61051 10-r/10-5 = 1.6105 - 1.3058/1.6105 - 1.2763 10-r = 0.304685/0.334228 x 5 r=10 - 4.558035 r= 5.4420 * 1985 - 90 = 107.6 x (1+r)^5 = 130.7 (1+r)^5 = 130.7/107.6 (1+r)^5 = 1.214685 To solve this use either compounded interest table or linear extrapolation or Pv function in excel We are using linear extrapolation here - r 5 year compounded amount of $1 5% 1.276282 r 1.214684 10% 1.61051 10-r/10-5 = 1.6105 - 1.214684/1.6105 - 1.2763 10-r = 0.395826/0.334228 x 5 r=10 - 5.921489 r= 4.0785 * 1985 - 90 = 130.7 x (1+r)^5 = 152.4 (1+r)^5 = 152.4/130.7 (1+r)^5 = 1.166029 To solve this use either compounded interest table or linear extrapolation or Pv function in excel We are using linear extrapolation here - r 5 year compounded amount of $1 5% 1.276282 r 1.166029 10% 1.61051 10-r/10-5 = 1.6105 - 1.166029/1.6105 - 1.2763 10-r = 0.444481/0.334228 x 5 r=10 - 6.649358 r= 3.350642 * 1995 - 2000 = 152.4 x (1+r)^5 = 175.3 (1+r)^5 = 175.3/152.4 (1+r)^5 = 1.150262 To solve this use either compounded interest table or linear interpolation or Pv function in excel We are using linear extrapolation here - r 5 year compounded amount of $1 5% 1.276282 r 1.150262 10% 1.61051 10-r/10-5 = 1.6105 - 1.150262/1.6105 - 1.2763 10-r = 0.460248/0.334228 x 5 r=10 - 6.885224 r= 3.114776 * 2000 - 05 = 175.3 x (1+r)^5 = 195.3 (1+r)^5 = 195.3/175.3 (1+r)^5 = 1.11409 To solve this use either compounded interest table or linear interpolation or Pv function in excel We are using linear extrapolation here - r 5 year compounded amount of $1 5% 1.276282 r 1.11409 10% 1.61051 10-r/10-5 = 1.6105 - 1.11409/1.6105 - 1.2763 10-r = 0.49642/0.334228 x 5 r=10 - 7.426356 r= 3.114776 * 2005 - 10 = 195.3 x (1+r)^5 = 218.1 (1+r)^5 = 218.1/195.3 (1+r)^5 = 1.116743 To solve this use either compounded interest table or linear interpolation or Pv function in excel We are using linear extrapolation here - r 5 year compounded amount of $1 5% 1.276282 r 1.116743 10% 1.61051 10-r/10-5 = 1.6105 - 1.116743/1.6105 - 1.2763 10-r = 0.493767/0.334228 x 5 r=10 - 7.386662 r = 2.613338 For part 2 - Monthly income X 12 X (1+.03)^years to retire This amount is future value of amount invested Please provide feedback… Thanks in Advance.. :-)
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