Independent solution

How to solve this Annuities and Perpetuities question

Setup

Setup

The payment in month k is 2k, and the quoted nominal rate gives a monthly effective rate of one percent.

j=0.12/12=0.01j=0.12/12=0.01

Model

Model

Factoring out two leaves the standard 60-payment increasing annuity-immediate.

X=2(Ia)60‾∣ 0.01X=2(Ia)_{\overline{60}|\,0.01}

Compute

Compute

Evaluating its closed form gives 1,237.30; restoring the factor two gives 2,474.60.

(Ia)60‾∣=a¨60‾∣−60v600.01=1237.30(Ia)_{\overline{60}|}=\frac{\ddot a_{\overline{60}|}-60v^{60}}{0.01}=1237.30

Answer

Answer

The annuity purchase price is therefore about 2,475, which is choice C.

X=2474.60(C)\boxed{X=2474.60\quad\text{(C)}}