Independent solution

How to solve this Monthly Savings Converted to an Annual Annuity question

Setup

Setup

Convert 8% annual effective to its exact monthly rate.

j=1.081/12−1=0.00643403j=1.08^{1/12}-1=0.00643403

Model

Model

Accumulate 240 beginning-of-month deposits to time 20.

F20=225s¨240‾∣j=128,848.5059F_{20}=225\ddot s_{\overline{240}|j}=128{,}848.5059

Compute

Compute

At time 20, the thirty-year annual annuity begins immediately.

F20=Xa¨30‾∣0.07F_{20}=X\ddot a_{\overline{30}|0.07}
a¨30‾∣0.07=13.2776741\ddot a_{\overline{30}|0.07}=13.2776741

Answer

Answer

The annual payment is 9704.15, choice B.

X=128,848.505913.2776741=9,704.1474X=\frac{128{,}848.5059}{13.2776741}=9{,}704.1474
X≈9,704(B)\boxed{X\approx9{,}704\quad\text{(B)}}

Calculator reproduction

BA II Plus keystrokes

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

  1. 240 · N; 0.6434030 · I/Y; 225 · +/− · PMT; 0 · PV; BGN mode; CPT · FV128,848.51Monthly accumulated savings at time 20.
  2. 30 · N; 7 · I/Y; 128848.51 · +/− · PV; 0 · FV; BGN mode; CPT · PMT9,704.15Annual annuity-due payment.