Question

g. Now let’s say you wait just 5 years before you start saving for retirement, how much will that cost you in interest? How about 10 years? How about just 1 year? (10 points) Now you need to consider if that is enough. If you live to be 90 years old, well above average, then from the time you retire, to the time you are 90, you will have to live on what you have in retirement (not including social security). So if you retired at 65, you will have another 25 years where your retirement funds have to last. h. Determine how much you will have to live on each year. Note, we are neither taking into account taxes nor inflation (which is about 2% a year). (5 points) Let’s look at this from the other direction then, supposing that you wanted to have $50,000 a year after retirement. i. How much would you need to have accumulated before retirement? (5 points) j. How much would you need to start investing each year, beginning right now, to accumulate this amount? A “short-cut” to doing this is to first compute the effective yield at your retirement age, then divide this amount into Part (i). This is the amount you well need to invest each year. (5 points) k. That was just using $50,000, how much would you want to have each year to live on? Dream big or reasonable depending on your occupation! Now using that value, repeat parts (i) and (j) again. You need to state what you would want to live on and it needs to be something besides $50,000. (10 points) Your answer to (k) would work, if you withdrew all of your retirement funds at once and divided it up. However, if you left the money in the account and let it draw interest, it is possible that the interest itself would be enough to live on, or at the very least if you had to withdraw some of the principle, the remaining portion would still continue to earn interest. Essentially, what you have found is the upper bound for the amount of money that you will need to invest each year to attain your financial goals. l. Finish by summarizing what you have learned in the entire project and consider setting a goal towards saving for retirement. (Your answer should be in complete sentences free of grammar, spelling, and punctuation mistakes.) This should be a paragraph not one sentence. (10 points)

Answer 1

Previously, we take P = $300 each year, r = 8% compounded annually, n = 1, t = 40 years.

And, the formula for the accumulated amount is :

g) If i wait just 5 years before i start saving for retirement, then the decreased interest amount is =

$[4050(1.08⁴⁰-1.08³⁵)-(5*300)] $26603.67

If i wait just 10 years before i start saving for retirement, then the decreased interest amount is =

$[4050(1.08⁴⁰-1.08³⁰)-(10*300)] $44230.55

If i wait just 1 years before i start saving for retirement, then the decreased interest amount is =

$[4050(1.08⁴⁰-1.08³⁹)-(1*300)] $6217.36

h) The required amount is = $[4050(1.08⁴⁰-1)/25] $3357.37

Therefore, I will have $3357.37 to live on each year.

i) The required amount is = $(25*50000) = $1250000

Therefore, I need $1250000 to have accumulated before retirement.

j) Let $P be the amount that i have to invest every year before retirement.

Then, by given conditions we have,

12.5*P[1.08⁴⁰-1] = 1250000

i.e., P[1.08⁴⁰-1] = 1250000/12.5

i.e., P[1.08⁴⁰-1] = 100000

i.e., P = 100000/[1.08⁴⁰-1]

i.e., P 4825.21

Therefore, i need $4825.21 to start investing each year, beginning right now, to accumulate the amount $1250000 before retirement.