Independent solution

How to solve this Arithmetically Increasing Annuities question

Setup

Setup

The ten deposits increase arithmetically from 1 through 10. Their time-10 value is an increasing-annuity accumulation.

F10=(Is)10‾∣iF_{10}=(Is)_{\overline{10}|i}

Model

Model

The same fund purchases a perpetuity paying 10, so its price is 10 divided by i. Use the increasing-annuity identity.

(Is)10‾∣i=s¨10‾∣i−10i(Is)_{\overline{10}|i}=\frac{\ddot{s}_{\overline{10}|i}-10}{i}
s¨10‾∣i−10i=10i\frac{\ddot{s}_{\overline{10}|i}-10}{i}=\frac{10}{i}

Compute

Compute

Thus the annuity-due accumulated factor must equal 20. Solving gives i = 0.1230407.

s¨10‾∣i=20\ddot{s}_{\overline{10}|i}=20
i=0.1230407i=0.1230407

Answer

Answer

The perpetuity price is 10 divided by i, or 81.27, which rounds to choice D.

10/i=81.27(D)\boxed{10/i=81.27\quad\text{(D)}}