Use the following information for all following questions unless they specify otherwise: Estimated inflation: 3% Estimated general US stock market return: 10% Estimated general US bond market return: 6%

As a reminder, we have so far the following formulas: Simple interest: FV = PV*(1+r*t)

Compound interest: Compound interest: Compound interest:

Perpetuity: PV = C/r Perpetuity: C = PV*r Perpetuity: r = C/PV

Growing Perpetuity: Growing Perpetuity: Growing Perpetuity:

FV = PV*(1+r)^t PV = FV/(1+r)^t (FV/PV)^(1/t) = (1+r)

PV = C/(r - g) C = PV*(r - g) (r - g) = C/PV ....

{Watch parenthesis!} So r = (C/PV) + g

And g = r - (C/PV)

Annuity: PV = C/r - (C/r)/(1+r)^t Annuity: FV = (C/r)*(1+r)^t - (C/r)

Annuity Due PV: (1+r)*Annuity PV = (1+r)* {C/r - (C/r)/(1+r)^t}

Annuity: C = PV / {1/r - (1/r)/(1+r)^t} Annuity: C = FV / {(1/r)*(1+r)^t - (1/r)}

Growing Annuity: PV = C1/(r-g) - (C2/(r - g))/(1+r)^t where C2 = (1+g)^t * C1 Growing Annuity: PV = C/(r-g) - {C/(r - g)}* {(1+g)/(1+r)}^t {Put all together}

Growing Annuity FV = (1+r)^t * {Growing Annuity PV} Growing Annuity FV = {C/(r-g)}*(1+r)^t - {C/(r-g)}*(1+g)^t

Growing Annuity C = PV / {1/(r-g) - {1/(r - g)}* {(1+g)/(1+r)}^t} Growing Annuity C = FV / {1/(r-g)}*(1+r)^t - {C/(r-g)}*(1+g)^t}

Answer the following questions

1) Given a set savings plan characterized by the following:

1) Ben is 45,

2) plans to retire at 67, 3) expects to live to 82 4) Currently has 200,000 in savings, 5) invested 80% stock market, 20% bond. 6) Ben plans to save an additional 10,000 per year, each and every year until he retires,

again investing at the same 80/20 ratio 7) Once retired Ben plans on investing at 60% stock and 40% bond

Preliminaries: A) What is Bens rWLE? {Remaining work life expectancy, aka t1} B) What is Bens RLE? {Retirement life expectancy, aka t2} C) What is Bens expected rate of return while working and saving {r1} D) What is Ben expected rate of return while retired {r2}

E) What will the current 200,000 savings grow into and become at the time of retirement, assuming it is continually invested with no tax loss along the way F) What will the additional 10,000 per year invested, each and every year until he retires, become at the time of retirement

G) Combining them, how much will Ben have at the time of retirement? H) If Benis interested in a constant income in retirement, what constant income C could this retirement savings purchase as a simple annuity? I) If Ben is interested in a constant income in retirement, what constant income C could this retirement savings purchase as an annuity due instead J) If Ben is interested in an increasing income in retirement, what starting income C could this retirement savings purchase as a growing annuity with a 3% growth rate (g = .03)? K) If Ben is interested in an increasing income in retirement, what starting income C could this retirement savings purchase as a growing annuity due with a 3% growth rate (g = .03)?

L) For answers H-K, find what the initial starting income C is in current dollars {Hint: PV = FV/(1+inflation)^t where C would be the future value and t would be t1}

Variations on above:

M) Suppose instead Ben invested at 100% stocks while working, repeat E-K with the new change

N) Return to the original r1 and the 80% stocks and 20% bonds while working and saving; however, now change the retirement savings plan to 100% bonds. Repeat E-K with this new change. {Hint: E-G should be unchange!}

O) Return to the original r1 and r2. However, have Ben live to 87. Repeat E-K with this new change. {Hint: E-G should be unchanged}

P) Return to the original life expectancy. Now have Ben retire at 65 instead of 67 (again still living to 82). Repeat E-K with this new change. {Hint: E-G should now be changed, as t1 has changed!}

Q) Return to the original problem but have Ben save 4% more per year (g = .04) from age 45 to 67. Repeat F-L

If spreadsheet is used please show all details.

If on paper please show all steps