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)}]](https://tex.z-dn.net/?f=OA%3DP%5B%5Cfrac%7Bq%5E%7Bn%7D-1%7D%7Bq%5E%7Bn%7D%28q-1%29%7D%5D)
Here <em>qⁿ </em>is:
![q^{n}=1+\frac{r}{Number\ of\ periods}=1+\frac{0.067}{4}=1.01675](https://tex.z-dn.net/?f=q%5E%7Bn%7D%3D1%2B%5Cfrac%7Br%7D%7BNumber%5C%20of%5C%20periods%7D%3D1%2B%5Cfrac%7B0.067%7D%7B4%7D%3D1.01675)
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](https://tex.z-dn.net/?f=OA%3DP%5B%5Cfrac%7Bq%5E%7Bn%7D-1%7D%7Bq%5E%7Bn%7D%28q-1%29%7D%5D%3D2000%5Ctimes%5Cfrac%7B%281.01675%29%5E%7B16%7D-1%7D%7B%281.01675%29%5E%7B16%7D%5B1.01675-1%5D%7D%3D2000%5Ctimes%5Cfrac%7B0.30445%7D%7B0.0051%7D%3D119392.16)
Thus, the amount to be deposited now to provide for this trust is $119,392.16.