7. Your friend is celebrating her 25th birthday today and 200.000drwaay intois r

Question

7. Your friend is celebrating her 25th birthday today and 200.000drwaay intois retirement at age 65. She wants to be able to withara he first we each birthday for 15 years following her retirement; in a retires on eaetreme birthday. Your friend intends to invest her m her anticipated her 66 which earns wants to start saving for r saving account on he will be on t withdrawal en account f year. She wants to make equal annual dn on the t account, or her retirement fund, Assume that the annua 8 percent before and afer her retirement. Ignore taxes and day and cotintal for the prdeposits e starts making these deposits on her 26th birthday and co total number o desired transaction costs for the problem. until she is 65 (the last deposit will be on her 65th birthat b able n her 65th birthday and the total number of annual annually to be able to make the desired problem is to first find the continue to make deposits deposits is 40), what amount must she deposit ann withdrawals at retirement? (Hint: One way to solve for this per year for 15 years that she needs to make from value on your friend's 65th birthday of the $200,000 withdraw after her retirement and then find the equal annual deposit her 26th to 65th birthday.) ) Suppose that whenever your friend makes the annual deposit to the retirement her employer will contribute $2,000 to the same account every year as part company's profit sharing plan. In addition, your friend will receive a $30,000 distributio from a family trust fund on her 25th birthday, which she will also put into the retiremen account. What amount must she deposit annually now to be able to make the desired withdrawals at retirement?

Explanation / Answer

A) First step will be to find the value of $200,000 withrawl per year for 15 Years at the age of 65 by using below formula

= PMT*((1-(1/(1+r)^n))/r)

Here PMT means annual amount required to be drawn every year i.e $200,000

r means rate of interest to discount i.e 8%

n means number of period for which payment will be done i.e 15 Years

Now, Value at 65th year = $200000*((1-(1/(1+0.08^15))/0.08)

=$200000*(1-(1/3.1722))/0.08)

=$200000*((1-0.3152)/0.08)

=$200000*(0.6848/0.08)

=$200000*8.5595=$1,711,895.7376

We have got the value required at 65th year, Now second step will be to calculate the Yearly amount to be deposited in next 40 years from 26th year to 65th year to get this value at 65th years

PMT= FV/((1+r)^n-1))/r)

Here PMT is the annual amount needs to deposited every year

FV is future value required at 65th year i.e$1,711,895.7376

R is rate of interest i,e 8%

N is no of year i.e 40 Years

Thus PMT= $1,711,895.7376/((1+0.08)^40)-1)/0.08)

=$1,711,895.7376/((21.7245-1)/0.08)

=$1,711,895.7376/(20.7245/0.08)

=$1,711,895.7376/(259.0565)

=$6,608.1940

So, She will needto deposit $6,608.1940 every year.

B)The Value of $30,000 receivedfrom family trust at 65th year will be

= $30000*(1.08^40)= $651,735.6449

Thus required amount at 65th Year will decreae by this amount

=$1,711,895.7376-$651,735.6449

=$1,060,160.0927

The New PMT will be

$1,060,160.0927/((1+0.08)^40)-1)/0.08)

=$4092.3892

Since $2,000 is submitted by employer she need to deposit $2,092.3892 per year

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