Question

2. Mrs. Jones wishes to fund scholarships for 10 students per year at the level of $8,700 per student. She wants the first scholarships to be awarded 4 years from now, and they should continue once per year forever. The scholarship endowment earns 4% per year.

A) How much must she deposit now if she will make no other contributions?

B) Suppose, instead, that she makes one deposit today and an equal deposit three years from now (but the scholarship plan doesn’t change). How much must each deposit be?

Answer 1

2.

A)First we find the present value of forever future scholarships at year 4

PV (at year 4) of future scholarships = Annual scholarship amount / Interest rate per year

PV (at year 4) of future scholarships = 8700*10/0.04 = $2175000

Now, to find the present value today, we discount this amount by the interest rate. This is the amount she must deposit now

Amount she must deposit now = 2175000/(1.04^4)

Amount she must deposit now= $1859199.11

B)

In this case, the present value of the 2 contributions should equal $1859199.11

Let the amount be X

Therefore,

1859199.11 = X + X/(1.04^3)

X(1+(1/(1.04^3)) = 1859199.11

X = $984225.88

Hence, each deposit should be of $984225.88

1859199.11