Question

Cousin Clara has been reconsidering her decision to become a nun. She still wants to
dedicate her life to helping people, but after speaking to several real nuns, she has
learned that the need for skills like “the Rigor mortis death chop” is rather limited at the
convent. In order to fulfill her life’s mission, Clara has decided to start a foundation to
teach young girls how to cope with the rough-and-tumble realities of the world, including
how to beat the snot out of boys who try to hassle them. The “You Go Girl Foundation”
will be eligible for funding by charitable organizations after it has proven its viability.
Clara wants to have the grand opening of the foundation four years from today (today
is January 1). Until then, she will work full time at her job with the credit company to
raise the funds necessary for the first five years of operations. After five years of
operations, the foundation will be eligible for grants to cover its entire operating budget,
but for the first five years of operations the budget will be self-funded.
Clara has a friend who will provide the office and work spaces at no charge, and he will
even pay for all utilities (Clara can be VERY persuasive when discussing charitable tax
deductions). The operating budget for the first five years will be $25,000 per year (Clara
will work part-time to cover her personal living expenses). This amount will be payable
at the beginning of each year since the folks who sell pencils and paper and bandages
cannot wait until year-end to be paid. Clara has opened an account for the foundation
at the First Philanthropy Bank; this account will pay 6% annually. All monies for the
foundation will be deposited in this account. Clara will make a deposit to this account
today and at year-end for each of the next four years (a total of five deposits); each
deposit will be for the same amount. How much must Clara deposit so that in four years
time there will be sufficient funds available to finance the foundation’s operating budget
for the following five years?
(In case you are interested, Clara won a small lottery prize and was able to put aside all
the money needed to send her nieces to karate school. She donated the rest of it to her
favorite charities. Good for her.)

Answer 1

In the given questoin clara wants to open a Charitabel Trust. To establish the same she needs to create the funds for the operating expenses of next five years.

The expexted Operating expense of the Charitable trust is of $25000 per year at the begining.

The Amount is Invested by the clara at the bank is 5 times starting from now i,e Time Zero and then after each year for four years.However the amount deposited by the clara each time is equal. Further the Interest Income Earned on abnk deposits is 6%.

Appltying the Concept of Time value of Money assuming that the interst easrned on deposit isalso earned on the interest component accoumulated year on year basis.

Here the Future value is given every year $ 25000 at the Beiginin of the year

PV = FV/(1+i/n)(n*t)  

Considering the PV of all the CAsh flows after 4 yaers to Zero time .

=25000/(1+0.06)(4)+25000/(1+0.06)(5)+25000/(1+0.06)(6)+25000/(1+0.06)(7)+25000/(1+0.06)(8)

=$ 88419.5465

Now, After deriving the prtesent value of all the expected cash out flows we need to compute the amount to be invested by the Clara every year to be able to get $25000 eavery year for next 5 years after 4 years.

We shall distibute the amount over five eaqual annual Installment which is the amount to be invested by the clara every year. As we obne installment we are paying at Time Zero we shall Consider trhe PVFA at the beigining of thee year.

Equated Installment = PV / PVFA(6%,5)

= $ 88419.5465 / 4.4651

= $ 19802.36

Hence, Clara Should Invest $ 19802.36 now at Time Zero and At end of the every year.

Logic:

The amount Invested at T0   will be receiving interest for entire 4 years. Hence the Amount Invested $ 19802.36 willl become $ 25000 at the beiging of the fifthe year T5.

Same way the Cycle goes on and the Amount Invested at T1 will receive inetrest income for next 4 years and will become $25000 T6 i.e. The begining of the 6 th year.

Assumption:

The Amount of Lottery ticket won by the clara and the remaing amount is equal to the required amount of Invetsment.