Question

Juanita Domingo's parents want to establish a college trust for her. They want to make 16 quarterly withdrawals of $2000, with the first withdrawal 3 months from now. If money is worth 6.7%, compounded quarterly, how much must be deposited now to provide for this trust?

Answer 1

Answer:

The amount to be deposited now to provide for this trust is $119,392.16.

Step-by-step explanation:

This problem is based on ordinary annuity.

An ordinary annuity is a sequence of fixed payments made, every consecutive period, over a fixed interval.

The formula to compute ordinary annuity is:

$OA=P[\frac{q^{n}-1}{q^{n}(q-1)}]$

Here qⁿ is:

$q^{n}=1+\frac{r}{Number\ of\ periods}=1+\frac{0.067}{4}=1.01675$

Compute the ordinary annuity as follows:

$OA=P[\frac{q^{n}-1}{q^{n}(q-1)}]=2000\times\frac{(1.01675)^{16}-1}{(1.01675)^{16}[1.01675-1]}=2000\times\frac{0.30445}{0.0051}=119392.16$

Thus, the amount to be deposited now to provide for this trust is $119,392.16.