Independent solution

How to solve this Changing Accumulation Rates question

Setup

Setup

Accumulate the ten equal deposits to time 10 at 6%. The completed fund then remains invested for five more years at 5%.

5000=Xs10‾∣ 0.06(1.05)55000=Xs_{\overline{10}|\,0.06}(1.05)^5

Model

Model

Thus the time-15 target equals X times the ten-payment accumulated-value annuity factor at 6%, multiplied by 1.05⁵.

s10‾∣ 0.06=13.1808s_{\overline{10}|\,0.06}=13.1808

Compute

Compute

The annuity factor is 13.1808. Solving gives X = 297.22, or 297.

X=297.22X=297.22

Answer

Answer

The calculation gives 297 for changing accumulation rates, matching published choice C.

X=297(C)\boxed{X=297\quad\text{(C)}}

Calculator reproduction

BA II Plus keystrokes

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

  1. 2nd CLR TVM; 10 N; 6 I/Y; 0 PV; 5000 ÷ 1.05 yˣ 5 = FV; CPT PMT−297.22END mode; reduce the time-15 target to time 10 before solving.