Independent solution

How to solve this Retirement Accumulation Annuity question

Setup

Setup

First translate the target number of shares and share price into a fund target of 310,880.83. Deposits occur at the beginning of each month, so the accumulation factor is an annuity-due.

F=3000(1000/9.65)=310880.83F=3000(1000/9.65)=310880.83

Model

Model

Use 300 monthly deposits and monthly rate 0.08/12. The fund equation is X times the 300-period accumulated-value annuity-due factor.

F=Xs¨300‾∣ 0.08/12F=X\ddot{s}_{\overline{300}|\,0.08/12}

Compute

Compute

The factor is 957.36657, giving X = 324.72. The listed monthly deposit is 324.70.

X=310880.83/957.36657=324.72X=310880.83/957.36657=324.72

Answer

Answer

The calculation gives 324.70 for retirement accumulation annuity, matching published choice A.

X=324.70(A)\boxed{X=324.70\quad\text{(A)}}

Calculator reproduction

BA II Plus keystrokes

Check END/BGN, period, sign, TVM, and cash-flow setup

  1. 2nd CLR TVM; 300 N; 0.6666667 I/Y; 0 PV; 310880.83 FV; 2nd PMT; 2nd SET; 2nd QUIT; CPT PMT−324.72Set BGN mode because deposits occur at the beginning of each month.