Independent solution

How to solve this Growing Monthly Retirement Annuity question

Setup

Setup

Accumulate the twelve monthly deposits within the first year to obtain the first year-end amount. Annual blocks then grow by 2%, while discounting uses the monthly rate 0.5%.

j=0.06/12,A1=2000s12‾∣ j=24671.12j=0.06/12,\quad A_1=2000s_{\overline{12}|\,j}=24671.12

Model

Model

Value the twenty-five annual blocks at time 0 as a geometric series with growth 1.02 and annual discount factor 1.005 to the power −12.

P=24671.12∑k=1251.02k−1(1.005)−12kP=24671.12\sum_{k=1}^{25}1.02^{k-1}(1.005)^{-12k}

Compute

Compute

The stream is worth 374,444. Compared with 374,500, it is short by 56, so the signed difference shown is −56.

P=374444,374500−P=56P=374444,\quad374500-P=56

Answer

Answer

The calculation gives the statement identified by the conditions above for growing monthly retirement annuity, matching published choice D.

P=374444(D)\boxed{P=374444\quad\text{(D)}}