Independent solution

How to solve this Annuities and Perpetuities question

Setup

Setup

Use the end of year 21 as the common value date and convert the annual effective yield to its equivalent monthly rate.

j=(1.08)1/12−1=0.006434j=(1.08)^{1/12}-1=0.006434

Model

Model

The beginning-of-month contributions form a 252-payment annuity-due; the four annual withdrawals form an accumulated annuity-immediate.

Xs252‾∣ j ¨=20000s4‾∣ 0.08Xs_{\overline{252}|\,j}^{\,\ddot{}}=20000s_{\overline4|\,0.08}

Compute

Compute

Equating their values at the final withdrawal date and solving for the monthly deposit gives 142.83.

X=20000s4‾∣ 0.08s¨252‾∣ j=142.83X=\frac{20000s_{\overline4|\,0.08}}{\ddot s_{\overline{252}|\,j}}=142.83

Answer

Answer

The required contribution is therefore about 142.80 per month, choice B.

X=142.8(B)\boxed{X=142.8\quad\text{(B)}}

Calculator reproduction

BA II Plus keystrokes

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

  1. 2nd CLR TVM; 2nd I/Y; 1 ENTER; ↓; 1 ENTER; 2nd CPT; 2nd PMT; if END is displayed, 2nd ENTER; 2nd CPT; 252 N; 0.643403 I/Y; 0 PV; 90122.24 FV; CPT PMTPMT = -142.83BGN mode; I/Y is the monthly effective rate and beginning-of-month deposits are negative.