# A university alumni group wishes to provide an annual scholarship in the amount of 1500 beginning...

## Question:

A university alumni group wishes to provide an annual scholarship in the amount of 1500 beginning next year. if the scholarship fund will earn an interest rate of 8%/year compounded continuously, find the amount of the endowment the alumni are required to make now.

## Present Value of Annuity :

Present Value is obtained using the formula : {eq}\boxed{P.V.=\frac{n\times P}{r}} {/eq}, where:

Number of payments per year {eq}=n {/eq}

Rate of Interest per year {eq}=r {/eq}

Size of each payment {eq}=P {/eq}

{eq}\\ {/eq}

Given : Number of payments per year {eq}=n=1 {/eq}

Rate of Interest per year {eq}=r=8 \%=0.08 {/eq}

Size of each payment {eq}=P=1500 {/eq}

To find : The Endowment Amount/Present Value i.e. P.V. .

Substituting the given values in {eq}\frac{nP}{r} {/eq} to obtain P.V. , we get :-

{eq}P.V.=\frac{1\times 1500}{0.08} \Rightarrow \boxed{P.V.=18750} {/eq}

Therefore, alumni are required to make an amount of {eq}18750 {/eq}. 